Poole. It has a fabulous harbour. It's beach runs from Sandbanks into Bournemouth, which runs into Boscombe, which runs into Christchurch. You can get a bus from Poole to almost anywhere. You can get the short local ferry crossing - at Sandbanks - over to the Isle of Putbeck - which a bus also uses - which then opens up amazing walks on the Purbeck peninsular.
It also opens up Swanage (my very favourite seaside town, as that is where we holidayed when I was a child), Corfe Castle, and stunning cliff walks to the west of Swanage Bay, which on sunny days has sea views and craggy rocks (and caves) that rival, or IMO surpass views of the Mediterranean!
The trains from Poole can take you West to Wareham and Weymouth & Portland, and beyond. The trains going East pass through Bournemouth, Southampton, and on to London. More local trains will stop at lots of places along the route. I once, when my children were little - one only a young baby - went by train from Poole to the New Forest with my DMum and DChildren (sorry I can't remember if we had to do a change or not between Poole and the New Forest), then at Brockenhurst in the New Forest, we changed trains to the ferry on the coast (sorry can't remember the name of the place, but it wasn't far), and then from the ferry we went to the Isle of Wight.
We stayed on a caravan site, and went all around the Island on buses, and had a brilliant week long holiday, then reversed the route back to Poole, and even with small children and all the baby's luggage it was a very easy journey; but I have to add here that I could not have managed it without my extremely Dear Mum, who is now very sadly departed.
The Dorset Coast has miles and miles of sandy beaches, but also dramatic cliff faces, and so many choices of lifestyle, that I can't imagine you ever being bored, whether you want those stunning walks, shopping until you drop, theatres, nightlife, busy or secluded beach time... I really can't think of any negatives except that I and my nearest and dearest don't live there anymore. If I won millions of pounds I would be moving back there immediately, and enticing all of my loved ones to do so too - I don't think they would need much encouragement!