I love Tulum, the temples are not as impressive as Chichen Itza or even Coba, (being a late post-classic period site), but being right on the coast, it's much more comfortable there than at most of the archeological sites that sit in the middle of the jungle. It's usually hot at the entry plaza, but once you are actually on the site, the ocean breeze really makes it nice.
You don't NEED to stay overnight to go to Tulum, unless you just want to. I've done both Coba and Tulum in one day. Just remember the archeological sites close at 4:00pm.
it's a full day, but it can be done. So if you're interested in just doing Tulum & seeing the surrounding area, staying overnight is not necessary. It would save you from having to pack an overnight bag & paying for an extra hotel night, when you have a perfectly good bed back on Coz that you are already paying for. unless you are planning checking out of your hotel in Coz, doing the hotel in Tulum and then going back and checking back in on Coz ... seems like a little much.
AND you will be already back the next morning so you can dive!
Take an early ferry over to PDC, & rent a car and drive yourself. You can even set up the rental car ahead of time with Isis Car rentals on Cozumel. They have an office in Playa as well.
You can usually hire your own private guide at most of the archeological sites in Mexico. We hired a private guide at Coba for $25 plus tip... or if you're sneaky enough, you can just slip in with one of the bus tours and get some free guide info. Just sort of stand off to the side of the group where you can still hear the guide talking.
I tried that at Coba. We got out of the car and saw 2 tour buses pull up. "hey let's just 'follow' them and get a little free tour!" I said. We walked up to the group and the tour guide started speaking German ... so THAT didn't work out