Let me preface this blog by saying I know very little about golf other than being an interested observer of the Open and the Ryder Cup. However, I know lots of people love the sport, so I've done a little
research on your behalf to show some of the golfing options available close to Drumlin Villa.
The first thing is, you're spoilt for choice with courses local to the Villa. A quick look at google maps shows there are 8 courses within 10 Kilometres.
Perhaps the most prestigious is Monte Rei Golf, a signature course designed by Jack Nicklaus. By all accounts the service and overall experience here is second to none. It's not cheap however, low season it will set you back 170 Euros ( a bit cheaper if you go before 9.30 am) and up to 200 Euros in high season. The green fees included shared buggy hire.
Quinta da Ria and it's sister course Quinta de Cima have green fees in the region of 75 Euro and are bordered on one side by the ocean. Benamor Golf, Castro Marim Golf, and Quinta do Vale all have fees in the region of 50 Euro.
Some of these courses can get extremely busy. As soon as you've booked your accommodation get your round(s) of golf reserved. Algarvegolf.net has a good summary of the courses, recent reviews, fees and availability.
Also, don't forget the Spanish options; Costa Esuri and Isla Canela Golf in Ayamonte. Remember the hour time difference though!
What about golf clubs? You can of course bring your own clubs with you and all airlines will accommodate you - for a price. The other option is to hire a set of clubs locally when you arrive. This company, clubstohire.com, is in the arrivals hall of Faro airport. I don't have any personal experience with them, but their Facebook page has good reviews.