I'm 6'1" and ride a 56 bike. How high should I have my seat? Right now, when at a standstill I can touch the 1st half of my foot to the pavement while stradling the bike. Should I only be able to touch the tips of my toes to the pavement? Would a higher seat help out with some burning in the knees?

Position yourself on the saddle with your feet on the pedals at the 6 o'clock and 12 o'clock positions. At the correct saddle height, the leg should be almost straight, but not locked, when the foot is at the bottom of the crank rotatation (6 o'clock position).
This is not an absolute rule. Some small adjustment may be needed for comfort, etc.
You may also have to adjust the saddle angle and fore/aft position.

You should have the saddle high enough so that your legs are almost straight at the bottom travel of the pedal stroke, but not high enough to have your hips rocking while pedaling.

See also https://www.sheldonbrown.com/saddles.html and scroll down a bit.

Go to your LBS. They can fit you correctly.

yes. Go read what sheldon says, it works.

they did. however, it was like "start here and see how this works"

My knees hurt all the time and have especially done so since I fixed my commuter. I recommend going higher rather than lower if your knees are hurting (assuming the pain is in the front of the knee). My seat hight is constantly changing so I can relate. Bring it up a mm or three at a time. You will find a sweet spot (for a while )

Burning in the knees could also result from spinning too low a cadence. If i remember correctly you are riding a SS so this is not as adjustable--the harder you must push to turn the pedal means more pressure on your knees. Higher cadence both puts less pressure on your knees and allows you to use slower muscle fibers (less force per revolution required) creating less muscle fatigue (burn). Read Sheldon Brown's article on cadence as a supplement to seat height for the described knee issues.

There is no exact rule for seat height. After following a certain set of general guidelines, you'll have to just raise or lower you set in cm or smaller increments until you find that sweet spot. The more you ride the more nit picky you will get about seat height. A good starting point for me is to have my seat high enough that I can just reach the pedal with my heal in the 6 o'clock position...Ride like that for a while and adjust accordingly. You should be able to solve your knee problem by raising it a cm or two.

i would definitely adjust your saddle relative to your pedal stroke, rather than relative to touching the ground. chances are, most of the time you're on the bike, you're pedaling rather than touching the ground.

The heel on the pedal trick will get you 99% there, at least that's how all 4 of my bikes are even though I didn't use that method to set them. I basically keep raising my seat until the backs of my knees start to hurt, then I lower it about 3mm. That seems to be the sweet spot. I also have my saddle positioned pretty far behind the cranks which made a huge difference in how my knees felt. I used to get all sorts of weird pains during and after riding. Moving the saddle worked each time (I learned by the 3rd and 4th bikes where it had to be).

HUGE DIFFERENCE. I raised my seat 1". Didn't think that would be drastic enough to tell, but DAMN! Big, big difference this morning.

56 seems like a smallish frame to me ... I have a 58 and probably next one will be a 60.

That must be a really long seatpost

If I quoted 56 before, I'm stoooopider than I thought. It's a 58.

I was just going to question the size. I'm 6'1" as well and ride a 59cm.

The way I check the seat hight is when the pedals are at 12 and 6, and the 6 oclock leg is slightly bent, if I push my heal down as far as it will go it should lock my knee. I use this when I set up my bikes and also when I go to spinning classes at the gym. It seems to work since I have never had any knee pain or discomfort. Just my 2 cents.

Mark