A short break is the one format where planning genuinely helps, because there is no slack in it. Two nights leaves you roughly a day and a half of usable time, and the single fastest way to lose a chunk of that is to stay somewhere that requires a bus to reach anything.
Stay central
For two or three nights, proximity beats character. The West Cliff and East Cliff put the pier, the Lower Gardens and the town centre within a walk, and drop you onto the promenade in minutes.
The neighbourhoods that reward a longer stay — Southbourne, Westbourne — are the wrong choice here. Their advantages are the advantages of living somewhere, and you are not going to be here long enough to collect them. The neighbourhood guide makes the comparison properly.
Do one thing well
The mistake on a short break is trying to reach both ends of a seven-mile bay plus the two towns either side. It turns the trip into transport.
Pick one direction and commit to it:
West — the chines. Durley Chine, then Alum Chine and its tropical gardens. Wooded, quiet, and a good half-day on foot from a central base.
East — the piers. Walk the promenade to Boscombe, have lunch there, walk or bus back. About half an hour each way on the flat.
Either fills an afternoon and leaves you with a coherent sense of the place rather than a list of things you glanced at.
The essentials
If you do nothing else: walk out on Bournemouth Pier, walk the promenade for at least half an hour, and eat one proper meal somewhere that is not on the seafront.
The Oceanarium and the Russell-Cotes museum are both close to the pier and both worth an hour, which makes them the right answer if the weather turns.
Book the accommodation, leave the days
Accommodation needs booking ahead, particularly for summer weekends, the Air Festival week in late August and the Christmas market period. A seafront restaurant needs booking at a weekend.
Beyond that, keep the days loose. Weather on this coast moves faster than a plan, and the ability to go to the beach the moment the sun appears is worth more than a schedule.
Related
Your first 48 hours in Bournemouth sets out a sequenced version of exactly this, and the events calendar shows what is on during your dates.