Hi Alex
St Augustine....been there on day trips from Orlando 4 or 5 times (last time 8 - 9 years ago though, pre kids). We absolutely loved this quaint little town.
Best bet is to go to the official tourist info centre first...it is signposted. Having picked up the leaflets get yourselves tickets for the little shuttle tram.....once bought these are good forever. The tram stops at about 20 or so stops and you can disembark and reboard another (services are frequent).
Our favourites;-
The Oldest Schoolhouse (how kids were taught centuries ago)
The Oldest Store (General Store of the 19th century)
The Fort (good displays)
Woolworths in the main square
Can't help you with where to stay...we only did day trips. Hotels/motels are plentiful though.
The tourist activities, depending on day trippers from Orlando, don't get into full swing until late morning and largely close down at night.
I would certainly love to go back there but a couple of hours of "when are we going to be there?" from the kids is off putting. Mind you, we bought a portable DVD in Orlando in October, so that might keep them occupied if we visit on our next trip, in July.