I've been going to Placencia every summer for years and love it, which I guess should be obvious. Like the rest of Belize, it is growing and "improving" but still retains its original fishing village vibe. I always dive with Splash and have become good friends with the owners/operators Patty and Ralph. Patty can help you with logistics, accommodations, etc if you need it.
You'll find the driving in Belize relatively easy since there aren't that many roads. You'll have two choices leaving the airport. You can either turn right on the Northern Highway and drive almost into Belize City, then at the roundabout take the well marked Western Highway towards Belmopan. Or you can turn left on the Northern Highway and drive up to the Hattieville road, turn left and connect up with the Western Highway in Hattieville. I prefer the latter route as it's faster and not as congested but finding the Hattieville turnoff might be a little tricky. I'm not sure there's a sign. I know there's a sign for the Baboon Sanctuary so you can look for that. From Hattieville, follow the Western Highway to Belmopan and hang a left onto the Hummingbird Highway. You'll go through the Maya Mountains, one of the two prettiest roads in Belize, with a number of one lane bridges. After you come out of the mountains, you'll turn right on the Southern Highway, well marked. Go to the roundabout, again well marked, and turn left. Follow that road all the way down the peninsula. Beware of the many speed bumps once you pass by Riverdale. Total time is about three hours.
A fun alternative when you drive back is to take the Coastal Highway shortly after you've turned left onto the Hummingbird. Not as pretty as the Hummingbird but it's gravel then dirt the whole way as you go through the coastal lowlands up to the Western Highway. Turn right when you reach pavement and proceed the way you came. The only bummer is if you have a flat or breakdown because you're a long ways from civilization, lol.
An alternative to driving is to take a flight on one of the two puddle jumper airlines, Maya and Tropic. No real difference between the two. Flights leave for Placencia about once an hour. And you can rent a car in Placencia from Placencia car rentals or Barefoot.
If you're into jungle stuff, like Mayan ruins, cave tubing, hiking in the Cockscomb Basin, then Placencia is a great choice. So is Hopkins, although accommodations there are more limited. If you can afford it, Hamanasi in Hopkins is a great choice but may be beyond your budget as I think it's on par with the resorts on Turneffe.