Westbourne is the most pleasant of Bournemouth's inner neighbourhoods, a leafy area of late-Victorian villas and a small high street about a mile west of the town centre. The traffic is slower, the cafes are independent, and the shopping is better -- antique dealers, a good bookshop, several delis -- than anything in the centre.
Westbourne Arcade, a tiny Victorian shopping passage, runs off the main road and is worth a look. The best fish-and-chip shop in Bournemouth, Chez Fred, is on Seamoor Road; the best Italian is half a block away. The area is within walking distance of Branksome Chine beach, which is the quieter half of the Bournemouth shore.