Looking to rent for a couple of months in Alicante

Hi people, Ill try to keep this simple and light hearted.

Me and my girlfriend are looking to rent a place from mid December for a couple of months (I'm 48 and she's 45). The thing is I have cancer and don't want to be too far away from the UK. Neither of us drive although I do have 2 Vespa scooters.
It would be handy to be in an area that has good bus routes trams or trains. Obviously a hospital near by would be very handy as expected. We both love outdoor life where we can find nice places to sit and watch the world go by, be that in a park near the sea anywhere really.
Neither of us speak Spanish but do try our best.

Earlier this year we went on holiday with her brother and his wife and it didn't go too well. so now i feel I should make the best of my rest and do this as soon as I can.

I've looked into the area of Alicante and it has the hospitals i hopefully wont be needing.
The thing We are looking for is accommodation near the sea front but not too noisy. something that could maybe accommodate us both and have a bed for our son if he wants to come over and maybe bring his girlfriend. We've also been thinking about Tenarife but its a little far although it would be warmer.
Any help, offers and advice would be brilliant.

Thanx Jim