Just rent a cart and take off. We've done it 4 or 5 times. Its as safe as anywhere else. Just stay on the main roads. Make the circle around the island. Be sure and go all the way to the other end of the island to Punta Sur. Beautiful overlooking the ocean with a very nice restaurant (Acantilado). Lots of cool roadside bars and beaches all along the way with cheap beer!
North beach on isla is great, take ferry from embarkadero it’s 10 min walk from TTR. You can walk beach to it also, takes a few mins longer. We go there every trip ( twice a year )
Theres a "beach". Probably not what you have in mind, but there is sand a water. And LOTS of seaweed. The nicest beaches are on farther south. The farther south you go, the more pristine they get. I can confess that there have been probably at least 4 trips where we didnt even go on the beach at TTR. No reason to unless you just want to chill and nap in a beach chair. The most time we've spent in the water was 3 years ago in July. The pool water was so hot, everyone was getting in the ocean to cool off. The fun is centered around the sexy pool. You'll have fun either way.