While most guesthouses and resorts have their own restaurants, there are also plenty of freestanding places worth trying. The serving portions tend to be huge, so don't be put off so much by the price as one serving is often plenty enough for two. Some of the food is excellent though the food at tour-group hotels tends towards buffets.
For seafood, Chonthicha Seafood is literally at the very end of the road at the southern tip of the island at Ao Yai. They do excellent seafood in a fishing port setting -- be sure to check the large nets hanging off the sides of the pier. Good for lunch or dinner. If full, Ao Yai Seafood (look for the sign reading "Menu All About Seafood") is a good second option, but it lacks the atmosphere of being right by the water. Both of these are a long way out of the way, but are well worth making the effort to reach. Bring your camera -- and an empty stomach!
A third option is Kreten Sea Food Restaurant, which is kind of in the middle of nowhere, a couple of kilometres to the north of Khlong Chao. The seafood is good -- we asked for our seafood salad extra spicy and boy did they deliver on that, but again the atmosphere lacks somewhat.
For more typical Thai fare with a northeastern tilt, Chiang Mai Restaurant is a couple of hundred metres south of Ngam Kho Resort (at the top of the hill, left hand side, look out for the bungalows) and does solid northern and northeastern dishes -- it's popular with songthaew drivers (always a good sign). Staff are very friendly and they even rent cheap bungalows. Just a shame it isn't on the beach!
Closer to the water (by Khlong Chao, north side of the bridge) you'll find Doy Bungalows Seafood (menu reads Duern Perfect Restaurant). We preferred Chiang Mai restaurant as they were friendlier, but this is very conveniently placed and does good grilled meats. Just around the corner (heading north) from here you'll find what we called Gai Yaang corner where there's a stall doing barbecue chicken and som tam for take-away only. There's a shop next door that does cheap beers for takeaway too.
Attached to the shop you'll find Relax Food & Drink, run by the affable Art. The short menu has some Thai standards and the owner is a great guy -- very friendly. You're also just a few steps from our favourite bar on the island, Tawan Eco Bar.
Last but arguably the best entry on the Thai food list goes to the restaurant at Ngam Kho Resort. The Thai food here is excellent -- don't be put off by the prices, as one serving is easily enough for two people. Staff are very friendly.
For coffee fiends, the Australian-Thai run Viewpoint Cafe should be your first stop. Previously on the headland above the southern end of Khlong Chao, they've moved to a new riverside setting right beside Sunset Bar. Dick and Wan are a very chatty couple, with a solid range of coffees (and other drinks) on offer. They're adding a couple of rooms that could be a very nice deal when complete. Another nearby option is Red Moon Cafe (next to Relax Food & Drink).
Ko Kut has little nightlife to speak of but we loved Tawan Eco Bar and its super-friendly and welcoming host Jong. Musicians will want to drop by for the nightly jam sessions, drinks are cheap (works on an honour system -- there's the fridge -- help yourself) and this is a good spot to meet others.
Nearby, other side and a little to the north, you'll find the aptly named Sunset Bar. Basically a wooden deck with a roof, it spills out into the mangroves and offers excellent sunset views. With low tables and cushions on floor, this is a very relaxed spot quite popular with travellers, though we preferred the music at Tawan Eco Bar. A third option in the area is Castaway Pub (opposite Away Resort). They have free WiFi which makes up for the otherwise lacking atmosphere and very slow service.
On Ao Phrao beach in the far south you'll find Rastafa Reggae Bar (between the two package resorts). It was closed the night we stayed on Ao Phrao and we didn't venture down to try it again, but it may be worth a visit. More obscure still is the ramshackle Bartist -- on the waterfall road and opposite PD Guesthouse. Bring mosquito repellent.