Car rentals start around $35-$40/day. If you're staying at the hostel, I have a contact that does drop offs and pick ups at the hostel included in his rate, and charges $45/day, without security deposit, rather than a freeze on a credit card. If you're traveling on your own, the hostel's a great spot to meet other travelers to split on the cost of a rental vehicle, which can make exploring the east end very cost effective. I also have a couple of coolers that I'm happy to lend out, if anyone wants to take a picnic lunch along.
So what's worth seeing while you're out exploring? Definitely check out Camp Bay- you might be the only ones on the beach, so it's a welcome change from the hustle and bustle of West Bay (no one selling you massages, bracelets or hair braiding).
While you have the car to adventure with, you might also want to check out Oakridge, with all the houses set on stilts over the water, and where the mangrove tours depart from. Along the main road, you'll see a huge pirate ship replica, which was (very briefly) a night club, until the owner was apprehended by the DEA, he was money laundering and part of a Mexican drug cartel.
There are some beautiful views as you drive along the east side. If you need a food stop, there are a few good restaurant choices. At Camp Bay, a bit east of the main public beach (a bit of a walk, you might want to drive further up), there's La Sirena, right on the water at the end of a dock. If you do the mangrove tour in Oakridge, you could ask for a stop at Hole in the Wall, a quirky bar/restaurant on the water frequented by yachties, that you can only access by boat (if you don't do the mangrove tour, drive into Jonesville to the very end, and ask someone to call them for you, and they'll send a skiff to pick you up). The Blue Mermaid Cafe is another option that's just accessible by boat- it recently opened, so I haven't had a chance to check it out, but it's on my list the next time I'm up that direction.
On the road heading out to Camp Bay, you'll pass Marble Hill Farms, where they sell a variety of tropical jams and jellies. If you're out exploring on a Sunday, check out Punta Gorda in the afternoon: it's the Garifuna village, and on Sundays, they do their dancing and drumming and sell some of their traditional dishes.
The Daniel Johnson Monkey and Sloth Hangout in French Cay is a fun stop (closed Sundays), and The Buccaneer in French Harbour is a great place to spend a few hours, in one of their hammocks over the water.
On the road connecting Coxen Hole to Flowers Bay (a road that runs parallel to the Sandy Bay road), there's the 'ROATAN' sign that you can pose by, as well as a cameo factory, and Steel Pan Alley is in that area, if you'd like to do a steel drum lesson.
On the road between West Bay and West End, you'll pass by the Roatan Rum Factory, and just across the road, the Lighthouse is a lookout tower with a beautiful view, costs a couple of bucks to go up and take a look.