When I push the pedals there seems to be a little bit of play.
Could that just be the crank arms or maybe even the bottom bracket?

Yes.

Entirely right, and no way of telling over the internet. Could even be the pedals themselves that are worn out.

I guess I'll just tighten everything one by one and ride around the block, to see what it was.

A description of the type of bottom bracket and cranks would help.

There are 3 items that could be at fault: pedals; crank connection to spindle; and the bottom bracket assembly. The problem is to determine which.

Pedals. Hold crank tight with one hand and try to wiggle pedal with other. Object is to find play between crank and pedal. If there is play it could be the pedal bearings or pedal not tightly screwed onto crank.

Cranks loose. Rotate cranks with pedals to 9 o'clock - 3 o'clock position. Push down on both pedals simultaneously with hands. Any motion of cranks relative to one another indicates loose crank on spindle. Rotate cranks 180 degrees and repeat.

Bottom Bracket. Try to rotate cranks side to side with hands. Any play indicates loose bottom bracket assembly or bearings.

If all 3 check out, then look for crack in frame near bottom bracket.

I have found that the best way to find the origin of any slop is to put your fingers on the parts you think might be loose so that it touches both parts while moving it. Your finger is VERY sensitive to the movement of relative parts that it is touching at the same time. This works for BB's as well as it does for headsets. Put your finger on the junction of the BB and the crank and wiggle the part(s). Put your finger on the pedal spindle and pedal junction and wiggle the part(s). Keep putting your finger on different areas and wiggling the relative parts until you can feel things move in directions/axis that they should not be moving or with more slop than it should have. Just keep trying until you find it.

Working on the pedals/crank/BB is much facilitated by a work stand where you can get the parts of the bike you are working on up to eye level and the rear wheel off the ground so you can move it freely in all directions/rotations. The source of the slop should become evident when you do these things. Bending over or crawling around on your knees with the bike on the ground makes it hard to see/feel what you are doing.

In rare occasions if after tightening the BB comes loose, dont overlook the fact that the BB may be egg shaped.

Ok, thanks guys.
Must be the bottom bracket. Pedals and cranks feel tight and I just tightened those again. Still feel the same when riding it.
Is there any way to fix that loose bottom bracket?

If it's the bottom bracket, both crankarms will feel loose.

Loosness in just the left crankarm is a frequent issue. If you're finding that it's important to immediately tighten the bolt that holds it. If you wait too long you will damage the crank arms interface with the bottom bracket and you'll have to acquire a replacement crank arm. The torque spec for that bolt is usually about 30 lb/ft. That's quite a bit. If you are trying to tighten that bolt with an Allen wrench that's only about 100 mm long, you aren't going to get to 30 lb/ft.

That's right, both crankarms feel loose.

In that case, I need to know exactly what kind of bottom bracket you have. If it looks like it has a lot of splines on the drive side, you have a cartridge. If that's the case, you need a new bottom bracket. They're not super expensive but it requires some bicycle specific tools to replace.

Hatta R9400 bottom bracket

This is a standard old school adjustable cup bottom bracket with bearings in a retainer. Here's a link to Park Tool's instructions for bottom bracket adjustment.

https://www.parktool.com/blog/repair-...racket-service

For the adjustment, you will need a lock ring spanner, a pin type adjustable cup spanner and whatever you need to remove the non-driving side crank. Not mentioned in the Park Tool article: tightening the lock ring will tend to make the bearings looser. You can make and adjustment quicker by over tightening the adjustable cup slightly before tightening the lock ring.

[QUOTE=SBinNYC;12123386For the adjustment, you will need a lock ring spanner, a pin type adjustable cup spanner .[/QUOTE]

Or a bladed screwdriver past its prime, or a drift punch, a hammer, maybe that pair of busted-up needle nose pliers you never get around to throwing and a roomy conscience...

How confident are you?

If it was my bike I'd gake the bottom bracket apart, clean it out good, and install new bearings in it. Using improvised tools, like dabac suggested, is fine. I wouldn't recommend buying special tools for this job because that BB design isn't common anymore and you'll probably never find a use for them again.

... unless you go out and buy more charming old bikes and then have to maintain them.

Nothing like experienced cyclists (who are confident in working on bikes) telling inexperienced cyclist to use inferior tools to learn how to work on bikes. The proper tools can be bought for $25 - $40. These tools should be used at least once a year to o'haul the BB. Granted the OP's BB probably needs less than 1/4 turn of the NDS cup then thighten the lockring. The proper tools will allow this procedure to be easy. Holding the NDS cup in place while the lockring is properly tightened is easily done -- with the proper tools.

Well, that's certainly one way of looking at the situation. Here's another:

When I started working on bikes I didn't have $25.00 to $40.00 to spend on bottom bracket tools so I learned to use what I had available. I still identify with people who have very limited resources struggling to keep an old bike operational.

IAWTC -Considering that for tools that might not be used again in a long time it can be done without them -AND OLSO be a learning experience at the same time.

The right tools make the job easier, that much is for sure. If someone learns how to do it the hard way just imagine how much better of a mechanic they become! All too often modern wrenches are only parts-replacer monkeys and have no clue how to actually FIX things without the fancy tools and all new parts. With all the latest whiz-bang tools and all new parts an actual monkey from the zoo could be trained to fix anything. They wouldn't know exactly what they were doing as the tool would be doing all the work -they'd just be pushing a button or pulling a lever.

Actually in Japan, that's still the standard bottom bracket installed in almost all Keirin frames. I think the tool wouldn't really be a waste in my case.
So bare minimum:
lock ring spanner,
15mm wrench
and a couple of screw drivers to to get the parts out?

to replace your BB? no that is not enough. you need;

a 15 (or 14)mm socket type wrench to take the crank arm bolts off.....CCW-5
a crank puller, a special too that screws into the crank arm and then pulls or pushes the crank off the spindle CCP-22
a lockring tool a special tool for tightening and loosening the lockring......HCW-5
a pin spanner for adjusting, removing and installing the adjustabel cup......HCW-4
a lockring tool with a long handle to remove and install the fixed cup................HCW-4

check the Park Tool website for the tools and a video. https://www.parktool.com/category/bottom-bracket