I live in Bournemouth.
Some great suggestions on this thread already…
Chez Fred is quite possibly the best fish and chip restaurant in the South, Westbourne is a little bit of a trek from your hotel though.
Westbourne is also home to a fantastic Indian fusion restaurant called Indi’s and a vegetarian place called Zucchini which serves lovingly prepared and reasonably priced food that should even appeal to ardent carnivores.
West Beach and Urban Reef are both excellent restaurants too.
Sticking with Boscombe (your hotel is at the mid point between Boscombe and Bournemouth town centre, both can be walked within 10 minutes), there’s Urban Reef’s sister eatery, Urban Beach. It’s a boutique hotel with an excellent (and very lively) bar/restaurant downstairs.
Reef Encounter is next to Sorted surf shop, a little further down Sea Road (heading towards the Pier/seafront), great ribs and American food, friendly staff.
Koh Tapas is on the edge of Boscombe and you’ll walk past it if you walk there from your hotel. Great Thai place with a tapas format so you can mix and match dishes.
Back to the town centre, Tapas Plus is a lovely Spanish owned/run tapas restaurant. If you’re in The Square (heart of the town centre) you walk past another tapas restaurant (La Tasca, not very good – chain restaurant) and head towards the town hall to get there).
Just around the corner (base of Richmond Hill) is a lively little Mexican place called Sombrero (formerly Coriander), reasonably priced and attentive service, food not bad at all either.
Old Christchurch Road plays host to lots ofthe usual chains (Pizza Express, ASK etc) as well as a few decent indies like local chain Alcatraz.
Head towards the seafront/BIC and you’ll find 60 Million Postcards on Exeter Road. Arguably the best bar in town, some good food too. Nice and informal. Great steak restaurant, ‘Steak out’ just across the road from there along with a couple of Italian efforts and Funki Sushi which serves Greek food…okay, it serves sushi.
If you end up in Charminster at any point (15/20 minutes walk up Richmond Hill) there are a load more tapas restaurants, Baraca which is a superb Moroccan restaurant, a brilliant Italian (the name escapes me, but it’s part-owned by Harry Redknapp and has lots of football memorabilia in the windows) and another great Japanese joint called Nippon Inn…terrible pun, but it’s a good place. There’s also a Thai restaurant just down from there in what estate agents are calling Lower Charminster (but everyone else calls Five Ways), it’s called Tuk Tuk.
Okay, that’s all I can think of right now!