We've always enjoyed the Blue Mermaid on the Hill, behind the Hilton Garden Inn in Portsmouth. Tasty and inventive fare, and the prices are very reasonable. They do a great plantain-encrusted cod with sweet potato hash and grilled banana.
If you prefer barbecue, try Muddy River Smokehouse on Congress Street.
Blue Mermaid Island Grill the Hills
409 The Hl, Portsmouth, NH 03801