It depends what sort of things you like doing. If you like things like walking and cycling, then you've got the New Forest or the Dorset Coast Path. If you like art, there's the Russell Cotes.
Southampton isn't far, nor Kingston Lacy for a National Trust house. Poole Harbour is great, and there's the whole of the Dorset countryside and loads of wildlife habitats.
It's also on the mainline to London- when I lived in Bournemouth, I often got the train up when I wanted to catch an exhibition at one of the big galleries. For me, the good things about London are things which can be done on day trips. Where I live, I want activities like swimming, gyms, evening classes, voluntary activities - that's all in London, of course, but also in Bournemouth, and they're good places to meet people. It depends what you mean by there being nothing to do- there's loads to do, but whether it's the sort of thing you want to do is a different matter.
You can keep in touch with friends if you move away, and make new friends. It won't be easy but it's not insurmountable.
I can understand where your husband is coming from. I grew up in south Dorset and also lived in Bournemouth for some years. The thing I miss most is being able to walk down to the sea after work, and in summer, have a swim (when most of the crowds have gone.) Winter beach walks are also great. It's not just me - I have schoolfriends who have moved back to Dorset from London to bring up their families. And I remember at uni, in a shared student house, I was saying to a girl from Cornwall about how I missed the sea, and she totally agreed. Another girl from Birmingham just didn't get it, and I think if you grow up close to the sea, you do develop a sort of need for it. I hated living in London, some of which was down to poverty, but also how dirty everything was. It's better now than it was then, with the congestion charge and so on, but I still wouldn't want to live there.
But it can't be a unilateral decision, so you need to work out what you really want from a place to live, then how Bournemouth or other towns in the area do or don't match that and have a properly informed discussion and a joint decision. Dorset may not be the only place to move to that might suit the criteria you come up with, especially if his includes "close to Lymington" and that is one factor which is ignored for the time being.