DontFALL57: My recommendation for you is the 24 inch FRAME SIZE of the 1970 thru 1976 FIVE SPEED Schwinn SUBURBAN.......the five speed!!!
Why? My belief is that you will likely find it more enjoyable to ride in comfort and with tourist handlebars.......rather than bent over in crouch with drop bars.

You won't be riding fast as you mentioned. The FIVE SPEED is all that you will need. The gearing on those Five Speed SUBURBANS are wide ranging which is great.
THEY ARE UNBREAKABLE! You should be able to locate one, purchase it and then replace the TIRES TUBES, BRAKE PADS, and if needed the BRAKE CABLES & SHIFT CABLE and SEAT if you don't like the factory seat for well under $220 TOTAL COST.........probably less than $200.
The FIVE SPEED SUBURBAN is so simple that you can easily learn to do all the servicing in ONE WEEKEND even if you've never before worked on any bicycle before.

The 5speed Schwinn SUBURBAN in 24 inch frame size from 1970 thru 1976:
Front Crankwheel has 46 TEETH
REAR WHEEL has the MODEL J freewheel
32---26---21---17---14

39**48**59***73**89 GEAR range as you see, You have a gear range between 39 and 89 which is wide enough and FIVE SPEED SIMPLICITY!!!


There is also a FIVE SPEED SUBURBAN in 1977 and later but it has the FFS system which works well but is non-standard in commonality.
For this reason, and to keep things simple, for this discussion concentrate on 1970 - 1976 5speed SUBURBAN model of 24 inch frame size.

I'd also say that you may not want the 1974 SUBURBAN 5 speed as for 1974 only Schwinn employed a handlebar thumb shifter on right handlebar instead of the Schwinn STIK stem mount. 1975 models returned to the superior Schwinn STIK stem mount. It is a matter of opinion as I do believe that the Schwinn STIK stem mount shifter is a better choice than the thumb shifter seen in 1974. Some people like the thumb shifter better, but I don't!!!

REALISTICALLY, YOU MIGHT FIND A 24" Frame SUBURBAN 5 Speed in READY to RIDE CONDITION for around $125, and some might say much less, as during non Covid-19 bike demand, probably a nice clean one for $75 to $80 but now during the Pandemic, you're looking at $125. The good news is that you are 6'-4 and most normal folks seeking old Schwinns prefer the smaller frames over the 24" as Schwinn frames are longer and accomodate larger riders than much more modern frames because of their relaxed geometry (angles of frame at seat tube and at headtube are pretty much parallel to each other)......thus the average 6 foot adult male can fit on a Women's 21 inch frame or a Women's 19 inch frame because of the seat-tube angle and the length between seat tube and headtube----what would be the top bar if it was a men's diamond frame.......
The 24 inch men's frame was widely sold back in the day when folks didn't care so much about the weight of an electroforged Schwinn.
These frames as are all of the electroforged Schwinn frames of 1966 and later, ARE INDESTRUCTIBLE!!!
THE STEEL WHEELS employed by Schwinn on these bikes are stronger than any wheels employed by competitors during that era.
My only advice is that you do want to look and see that the spokes appear to be clean and free of corrosion....

You will find that the ONE PIECE FORGED STEEL ASHTABULA CRANK is unbreakable and simple to service the two #64 (number sixty-four) crank bearings.

The factory rear derailleur is nearly bulletproof and supremely durable.
It is made by SHIMANO for Schwinn. 1970-1973 and very early 1974 models have the GT-100 rear derailleur, and the 1974-1976 models have the GT-120


Okay, now if you did want to improve your hill climbing ability over what you have from the factory's 46 front crank and 32 teeth rear (giving 39 GEAR)
You could easily install say for instance something like a 44 teeth front crankwheel or 42 or anything less than 46 as there are so many crankwheels available for Ashtabula one piece cranks since so many bikes and cruiser bikes have employed Ashtabula one piece cranks since at least the 1930's, and the one piece crank was once a fixture in the early days of bmx.


There are plenty of tire options in the 27 (630mm) range for the Schwinn steel 27 inch rims as seen on the SUBURBAN.
Sure, you won't find anything in 27 inch in your local bike shop but every major online bike shop and major online bike parts/online bike shop sells the 27 (630mm tires) by all the major manufacturers.......you can get street tread, to something suitable for dirt/asphalt/gravel which is semi-knobby....
One thing is that some tires like the MICHELIN PROTEK 32-630mm 27 inch tire will not clear the stock fenders on a Schwinn Suburban...... I have the Michelins on a 1971 Suburban. On that Brown '71, I have it fenderless. The MICHELIN PROTEK is a great basic pavement or paved path tire but I would say that you don't want it on dirt or gravel......there are other tires with suitable with tread for that and you'd need something with aggressive tread for dirt and gravel...
Depending upon whether you choose to keep the fenders, you may have to inquire about that with the seller and manufacturer's details etc...............most 27 (630mm) tires seem to fit the SUBURBAN and have no problem with fender clearance........I know the Michelin Protek will not without rubbing.

Yes, I am certain that numerous others will chime in and say that Vintage Schwinn is nuts. My belief is that it will give you a great starting point to the enjoyable type of leisure riding that you wish to do. The bike will be supremely durable. Yes it weighs a frikken ton (40 pounds) compared to a modern road bike or even a modern hybrid. Its unbreakable, durable, and never misses a beat, sort of like the Keef Riffhard of the bicycle world......what Keith R. does is really basic and simple yet look at all he's done with that five string tuned to G approach in addition to normal tuned stuff. Simple and durable is just what you need to roll.
The bike will not cost you much to acquire. You likely can find one in or near your area within three weeks.
HECK, IF YOU'VE ALREADY GOT SOMETHING IN A WALMART- DEPT STORE TYPE BIKE THAT FITS YOU COMFORTABLY AND IS DEPENDABLE, KEEP RIDING THAT BIKE!!! A bicycle is a bicycle if you're not racing it, or if you're not trying to keep up with a pack of riders on speedy lightweight road bikes! Yes, if you're trying to impress your pals or you want to fit in with that circle of rider on speedy lightweight road bikes, oh heck yeah, the ancient old Schwinn ain't gonna do that unless you've got street cred of having placed and won triathlons ( on racebuilt bikes of course-not an electroforged Varsity) and you're just showing off that you can maintain the pace of the pack on an ancient Schwinn while on group rides with average riders. ....Yeah thats always kinda cool when the campy Bianchi boy that is much younger can't keep up the ancient tri-athlete riding the electroforged Chicago battleship. It's the same as playing some cheapie old Teisco, or no-name or Squier or even some walmart Worst Act electric guitar on stage......if you're a good guitar player, it is gonna sound good if the guitar is playable and reasonably set-up properly.............if you can't play and your band isn't ready to leave the garage just yet........well, you can get the best instruments, PA and best equipment in the world and you're still gonna sound like dog dew , no matter what.

This is only a suggestion. It certainly is a decent low budget, cost effective solution that will prove extremely durable and reliable.
There are certainly other ways that you could proceed, rather than considering something ancient.
It is ultimately your choice because if you're not having fun, you're doing it the wrong way......
Go with whatever gives you the most joy and fun. Ultimately, that is money well spent if it gets you out riding often when the sun shines and the weather is nice!
Even if you do exceed your initial budget slightly, if it makes you happy, and you have fun riding....why not....if the added expense is easily swingable at this point in time. If you enjoy riding your current bike, just forget about what store it came from and just continue riding it. There is no hurry to dump a load of cash on something new that might not be any better than what you already have for the recreational, fun-time riding that you intend to keep doing. Keep the cash and you can still have fun on the two wheels you've got. You'll know when, when you know....until that time comes, just ride and have fun, as you're not out to impress anyone......
You can always get a repro decal set for an "acceptable" marque to give an instant upgrade to your existing bike to confuse 'those' who may think it is a BSO based on its current factory decals but with the decal upgrade-headbadge change upgrade will love it......... .....silly and stupid, but often true as many of 'those' yo-yo's only recognize the large black lettering decals on certain bikes and can't distinguish between anything else.............