£60k a good house?! Have you missed a 0 at the end? It's out of my imagination! Even in the very rural part of seaside Kent £60k can't even get me a flat! What city do you refer to? Is it somewhere without job opportunities?
Also you mentioned that it's half-hour drive to the city centre. Is it a rural road or motorway? How's the bus service along that road?
My requirements are follows, in no particular order:
1. good regional transport network
2. have job opportunities
3. close to a year-round lido
4. not far from low-cost airline airports
5. easy access to a seaside beach
Bournemouth only has 2 out of 5 (items 2 and 5).
Brighton has 4 (item 3 is missing).
London has 4 (item 5 is missing).
I don't think there is a place in the UK which has all 5, but it's possible in other countries.
So I decided whether a lido or a beach is more important for me in terms of my marathon swim training, and the answer was very clear that without a lido I can never get my swim training done properly, as evidenced by my life-regretting failure last year. So I choose London.
Most lidos are concentrated in London and in its commuter zone but there are also a few in the North. But I don't think they are located in places with good regional public transport, and not far from a good selection of low cost airlines for longer-distance travel as well.
Firstly, I didn't necessarily say you would get a good house for £60k. I'm renting my current place (with a few others in the house too) for £400 a month for a room in a huge Victorian terrace in the best area in Newcastle. If you're looking to rent you can easily find nice places for under £800 per month. £60k is about the minimum you can expect to pay for a decent one or two bedroom flat in the city itself, but looking a little further afield on Rightmove you can find two bedroom houses for as little as £35 - 40k in places like Easington and Peterlee, about 30 mins drive from Newcastle by car, 40 mins by train or just over an hour by bus. There's also the much closer but smaller city of Sunderland within 20 mins by bus or train. Of course, if you're paying less than £50k for a house you have to have low expectations and be prepared to spend a bit on making the house nice to live in, but if you're looking for an area with low living costs, it doesn't get much better than this!
In relation to your requirements, Newcastle has :
1. One of the best regional transport networks in the UK, the Metro is the second busiest urban rail network in the country and Newcastle station has direct trains to London, Edinburgh, York, Manchester, Liverpool, Birmingham, Bristol and other major places.
2. Plenty of good job opportunities in many different industries. "The North" got a bad reputation for having no jobs during the 1970's and 80's but the reality is very different today. Don't expect a London salary but as I stated the living costs are so much lower that you'll have a lot more savings and probably less commuting time.
3. Think this is the one requirement that Newcastle fails on. I don't think there are any lidos in the area but there are some excellent indoor pools.
4. Newcastle airport is around 15-20 mins from the city centre using the Metro. Flights go to at least 25 different destinations all over the UK and Europe.
5. Plenty of beaches along the coast - Whitley Bay, Tynemouth, South Shields, Roker, Seaham just to name a few. For a proper "seaside" experience, Scarborough is about 2 hour's drive away.
Of course, as you stated you're not going to be able to find somewhere that fits all of your categories. As you said here :
as evidenced by my life-regretting failure last year. So I choose London.
You don't want to regret another decision regarding a location to live in. Sure, London has its positives, but do the benefits outweigh the huge costs you have to pay for living so close to the city? I'm not trying to say that the North is perfect in any way - it has plenty of problems that you won't experience so much in London - but I think you might want to examine the other options available to you before making any big decisions about finding a place to live or buying a car (just realised that I've gone completely off topic here!). I think (please correct me if I'm wrong!) that you haven't really even considered that there is more to the UK than just London - based on the fact that you think that a house costs over £400k!