If you are prepared to travel to the western Algarve (transfer about an hour) Lagos may suit. It's not a typical 'Brits abroad' resort and still has some Portugese flavour to it. Many restaurants & bars in small winding streets.

Various apartments can be hired. I stayed at the Marina Club which you have to DIY as it's not in the brochures. My review is here under the name of Chris.

http://www.holidaytruths.co.uk/reviews/portugal/algarve/lagos/marina-club-apartments/

Other popular apartments are Vilabranca which can be booked through Thomson and FC. The main 4* hotel is the Tivoli Lagos, so if you want a hotel you could read reviewson it.

If your 2 year old is in a buggy, the cobbles in Lagos town might be a problem. If that's the case, you could try the 'old town' part of Albuferia which is supposed to be a lot more authentic than the strip area. There are some apartments called Brisa Sol which are in all the brochures & seem to get good reviews located halfway between the old and new town.

FC are also opening one of their Holiday Villages a little way outside Albuferia, these normally have great kids facilities & might be worth investigating, but could be a bit touristy for you. There is a thread on here about it. Used to be called Club Alto de Colina. (I think)

I also like Vilamoura, it has good quality hotels, a beautiful marina & good beaches. Some say it's not authentic as it's purpose built, but this means it has an upmarket feel to it, nice landscaping & good restaurants. Its also flat unlike a lot of places in the Algarve.

Hope this helps a bit. Doe