Hi Jim and congratulations on moving up your timeline.
I used to live in Cabanas de Tavira, a nice little seaside town just 8 km east of Tavira. Cabanas has an amazing beach, plenty of good restaurants and everything in walking distance. Tavira itself is a lovely old town with lots of Roman history, all the major supermarkets are represented, good medical centres and again, plenty of good restaurants. There is a regional railway that runs all along the coastline and very easy to hop from one town to the other if you don't fancy driving. Also, lots of good walking along the mainly flat coastline. I am not a golfer but there is an excellent course (I'm told) just outside Cabanas and several other courses within 30 minutes drive. A few years ago I had 3 British golfing friends to stay. They played 3 of the local courses, rated them all excellent and said that the prices (even as guest members) was much less than they pay in UK.
In terms of cost of living, I recommend you watch the recording of this recent webinar, USA vs Portugal: Let’s compare the cost of living which you can find from this link:
We also have an upcoming webinar, Cost of Living in Portugal: Supermarket Shopping on 12 November and you can 'reserve a seat' from the same link.
In my opinion, house prices in East Algarve are generally cheaper than West Algarve. Prices in Sesimbra are likely to be similar to East Algarve. But a lot will depend on the house condition (obviously) and how close you are to the sea.
I hope this gives you a good starting point Jim. If you can do it, nothing beats renting for a few months in each area before making the final decision.