Hi colinbredin ... regarding weather, taxis and various means of transfer from the airport, etc., you should find some useful info and links in these topics:

Weather Q&As
Alicante Airport, Q&As, Resort Transfers

As for your accommodation, the Hotel Marina first sprung to mind, but it is not in the Old Town. I am still trying to think of a Marine Hotel located in the Old Town.
David

Depends when you are going in November as there is a festival which I think is the first or second Saturday of the month through to the following Wednesday. It gets absolutely jam packed around that time. We were there last year and it was very busy - all the pubs were full. On the Thursday it's fancy dress day and absolutely everybody gets dressed up. There were some excellent costumes. Following the festival it did seem to get quiet - I think a few pus close down and then re-open just before Christmas, but there are plenty that are still open. The weather was very good - t-shirts and shorts during the day but needed a cardigan or jacket and jeans in the evening. Can't comment on transport as our transfers were included.

Family going to Beni for a weeks break 1st week in November staying at the Marina Hotel. This hotel only has an outdoor pool so I amagine it will be too cold to swim in. But is there somewhere we can go to get a swim and just chillax.

If I remember correctly, the Rosamar has an indoor pool and spa which you had to pay extra for so I would imagine it's open to visitors and not just guests.

luci

The Hotel Helios has a covered pool that non guests can use. It was 2 euro's for a day ticket a few years back.