This post probably would have been better posted on the Algarve Forum.
As regards a good restaurant in Faro, try the Adega Nova.
Details here:
http://barlaventostravelblog.blogspot.com/search?q=Adega+Nova
Also have a look at this hotel, also only three short blocks from the Station.
http://www.residencialalgarve.com/
You asked for a hotel near the airport. To be honest there aren't any at present. The nearest is in Montenegro 2 km away. The Faro Ibis is between the Airport and Faro. One can walk from there to town but it is a bit of a hike.
If you are taking the train to Funcheira, you would be better off getting a hotel in town from where you can explore Faro and easily get to the Station as the local buses in Faro are nothing to get excited about.
