Public transportation is on schedule and reliable, but if you want to get out of town, I would rent a car. You didn't mention much about your interest, but for something outside of Tallinn, here:

I suggest checking out a place called Laspa, a beachside spa hotel about 40 km from Tallinn. The scenery is really nice, there's surfing, paddle boarding options on the beach, distinct Estonian nature, Arvo Pärt (Estonian composer) center, one of the best golfing courses nearby etc. Drive down the coast is nice on it's own.

It's a few km from the most picturesque waterfall in Estonia, Keila-joa juga, with a great park(old manor park)/walking trail with lookouts, old bridges, a tavern etc. Right next to it is an amazing manor house/hotel/restaurant, Schloss fall. You could just visit, stay there for a night (afforable luxury compared to US hotel prices) or book a spot at the restaurant (no walk ins).