Hello shrimper, most of the resorts here are as you say a bit hilly, the one I would put forward for you would be Lagos. one end of it does rise up a hill but if you pick your hotel right you can keep away from the hill.
I would have a look at the Tivoli Lagos nice 4 star and do the B&B so you can go to some of the nice restaurants at night.
This hotel does a free bus service to there own part of the beach, with a bar and toilets and free sun beds that saves about 15 euros a day, we have been here and are thinking of going back next summer, there is a nice pub just out side the hotel that has singers and karaoke on most nights, good place to end the night and there are some good restaurants near it if you don't want to go into town 10 minutes.
Dave.

I really enjoyed our 3 stays in Lagos too. We stayed at the marina in a private apartment ideal for getting into town of an evening.

There's also always a nice breeze in Lagos which is very welcome when it's high summer temps.

How about Vilamoura, not stayed but visited the Marina area each time we have been to the Algarve.

I've often seen it as the recommended resort for those wanting somewhere flat, and there are a few nice hotels around the marina area.

We've stayed in Praia de Luz, Cabanas and Lagos but all of these can be a bit hilly in places, and the old town part of Lagos is cobbled which can be a but if a nightmare for walking difficulties or someone who gets arthritis in their feet (like I do).

Cabanas along the front is flat but there are beach issues there as you have to get a little boat to the beach which will make it unsuitable if easy access to the beach is important.