I've lived in the Bournemouth/Poole/Christchurch area for most of my adult life and I went to university in Southampton, so I know this area fairly well.
There are two things that a lot of people don't realise about Bournemouth/Poole/Christchurch: namely that it isn't really three separate towns, and that it is a lot bigger than you think: if the area had city status (which I expect is probably on the cards at some point), it would be the largest city on the south coast, surpassing Southampton, Portsmouth, Plymouth and Brighton.
The positive things about the place, in my view, would be:
The location: it's right between Dorset and the New Forest, and is positively surrounded by areas of outstanding natural beauty. It's also only about an hour and a half to London on the train.
The beach: a Bournemouth resident, on travelling to less fortunate places like Brighton, is duty-bound to sniff disdainfully before saying "call that a beach?". Almost ten miles of golden sand: none of this pebble rubbish. There's also Poole and Christchurch Harbours, both of which have lively watersports scenes.
The climate: we genuinely seem to have a favourable microclimate here. There's also the fact that Bournemouth is one of the "greenest" cities that I've ever lived in - not in the sense of ecologically conscious but rather in the sheer number of parks and just trees everywhere. I think it's cool that where most other cities would put a shopping precinct (I'm looking at you, Coventry), we have two miles of gardens stretching back from the beach.
The diversity: surprisingly, the conurbation has thriving and very visible Middle Eastern and Eastern European communities. It's also a very "young" place, with two universities and a large number of language schools catering to foreign students of English.
The negatives, however:
The inequality: Poole in particular is shocking for this - Sandbanks is one of the most expensive areas in the world to buy a property, while Turlin Moor is one of the most deprived areas outside London.
The politics: my god, this is Toryville. You could literally put Satan himself in a blue rosette and he'd be voted in. That said, the local council (which is new: merging the previous three town councils into one was essentially a Tory project) is not Conservative-led.
The cost: this is an exceptionally expensive place to buy and rent.
The drugs and the associated problems: Bournemouth in particular has a higher than usual number of drug rehabilitation clinics (notable alumnus: Gazza). Unfortunately, they don't seem to do a particularly good job. London boroughs in particular will fund someone with addiction issues to come to one of the Bournemouth clinics and then essentially wash their hands of them, which leads to high rates of single homelessness, drug-dealing and associated crime.