Colombo hotels - Stay at the Cinnamon Grand or the Taj. Pretty chilled out atmosphere and great restaurants at both of them. You could even stay at each one at either end of your stay. Try and have a few cocktails on the beachfront at the Galle Face Hotel, but avoid staying there. It's time is past. Mount Lavinia is ok, but it's just a colonial hotel that's more about the setting than the food, or the luxury.
Wouldn't advise driving if you're not used to somewhere like London or if you've not driven in Asia before. The Highway Code is treated as a suggestion, not law. If you get in an accident then you're a bit ****. Renting a van and driver is fairly cheap and hassle free. The hotel may even be able to sort you out with one. If you do rent, then get a 4x4 because the roads are crap.
West coast, Hikkaduwa and onwards is pretty good. Bentota is very resort-ey, but still ok. Even Hikka is a bit touristy these days, but the beaches are still lovely and the further away from Hikka and towards the South you head the more unspoilt the beaches are. Hotels are still cheap. Try and avoid the beachside cafes for food because they're shit. The street food, and smaller restaurants away from the beach serve better food.
South, well, not that much experience of it, but I hear they've spent a ton of money on infra there because that's where the president is from. Probably worth a trip.
East coast is a jewel. Trincomalee is a must to visit. The seafood there is incredible. Book a little boat trip to the little islands during the day. Few things are more fun than being on your own little island with a vast blue expanse of sea in front of you as the sun beats down on you.
If you do head into the hill country (your post makes it sound like you're making your way round the coast) then check out Adam's Peak. It's a bit of a climb, but it's cool to see the sun come up at dawn over the peaks. You can also do the classics like the elephant sanctuary, tea and spice factory tours and the temples if you want, but temples are temples and factories are factories anywhere in the world.
- Be prepared to pay "White Man Tax" on tickets for attractions.
- When people shake their head from side to side then they mean yes.
- Sri Lankan people are pretty smiley.
- Tell anyone at temples asking for a donation to **** off.
- Try some of the Sri Lankan arrack.
- Try the pub quiz at The Inn On The Green. It's... interesting.
- Try a chicken koththu if you like spicy food.
- You get a better exchange rate changing your £s or $s at a jewellers than at the airport, or buying them from here.
- Tap water is drinkable, but perhaps best not to chance it.
- Don't order anything with sausages or cheese. They're all processed shit.
- Shopping is shit. Don't bother with any of the department stores thinking you're going to find bargains.
- If you smoke or are planning on a few cheeky tipples in your hotel room then take advantage of the duty free.
- Try and fly direct. Stopover in the Emirates is a ballache. Sri Lankan are ok to fly with.
- Be prepared to see some of the most horrible shit in the middle of the most beautiful places. Beggars with disabilities, starving kids, stray dogs, cows all that sort of thing.