I'm biased because I live in Devon but it's a really beautiful place and around Exeter you have the best of both worlds - accessible to beach and Dartmoor but with good transport links too. My DH often works in London (precovid) and finds the trains good - some only stop in Reading then London.
Exmouth is not run down like many seaside communities can be - it has an M&S food hall right by the station! Though it does have its empty shop corners of course. The Exe Estuary cycle path is really stunning and you have really 'naice' pubs such as The Puffing Billy at Exton along its route. Villages such as Woodbury and Lympstone are chocolate box perfect and Budleigh Salterton is really lovely and walkable or cyclabke from Exmouth along a traffic free cycle route.
Exmouth has good amenities, both in the town centre and outskirts - there's a large Tesco, Lidl and assorted stores like The Range and Home Bargains in shopping centres further out and lots of independent shops and a tesco metro etc in the town centre. There's a swimming pool, decent library, several doctors and a cottage hospital with minor injuries etc. It's very easy to get to Exeter for John Lewis, IKEA, Marks etc.
I am not from Devon originally so maybe I mix in the wrong circles to know about this stuff, but I have a very diverse mix of friends and acquaintances/work colleagues who originate from all over the UK and globe and there's never been any issue re 'outsiders'. Exeter is a university city with a large international cohort and the university (precovid) hosts large events for different cultural celebrations such as Diwali and Chinese New Year. Devon as a whole lacks diversity but I would say that I have witnessed more unpleasant acts related to racism in other places I've lived such as Nottingham and North London. Exmouth certainly doesn't have the cultural offering you may get elsewhere - galleries, museums, cinemas and theatres are small but we travel for these things and make a weekend of it, and also take advantage of Plymouth and Bristol's offerings as day trips. We really enjoy the outdoors and in Exmouth you've got the sea on your doorstep along with Woodbury Commons and Dartmoor a short drive away.
The housing range in Exmouth is good so you should find something to suit you in budget, although Devon's house prices do seem to be going up put of kilter to other areas.
My parents in law (both sets) live in Kent - one lot inland and one lot coastal. DH also has uncles and aunts living in Sandbanks and Folkestone. Folkestone has a lovely coastal park for dc which we've really enjoyed, but I find it really hard to find family places to visit and eat out around Folkestone. Both sets have commuted to London a lot and so value the rail links and proximity but I find the SE very congested and expensive after experiencing the SW!
I'm v biased though, you couldn't drag me out of Devon now!
Good luck with your choices :)