I think the Old Town is definitely the right choice for you. It would suit your requirements perfectly.

As far as accommodation is concerned, you could look at any apartments in the Old Town or up above it on the main dual carriageway (Avenida dos Descobrimentos) which is about 15 minutes' walk from the beach minimum. Alternatively, there are lots of apartments up on Cerro Grande, which is the headland between the Old Town and the Marina - these are about 8-10 minutes' walk from the Old Town - and you did say you didn't mind steps!
You might find this interactive map useful to get your bearings.

Old Town definitely IMO

Yep, Old Town for sure!

For the last two summers i have had a 2 weeks stay at the Brisa Sol hotel located ideally between the New and the Old towns , smashing hotel with half board or self catering , nice and quiet but near enough to the action , only a short walk to either , or use the tourist train that stops right outside the Brisa Sol cheers paddy

As always - great replies, Old Town sounds like the right place, also going to have a look for Brisa Sol (sounds like best of both worlds)

Cheers

Santa Eulalia is also well worth considering.
(In fact, my family and I think the area is ideal - we love it.)

It's a VERY friendly area, very popular with locals of all ages,ALWAYS a good sign) families and
couples (both locals and tourists.)

It's right by the beach, has some fabulous restaurants and great bars in the immediate vicinity.

You can get the (air conditioned) bus into the Old Town for €1.10 or a taxi for €4 (approx)

There's also a good ticket agency next door to the well stocked, reasonably priced supermarket,
were allsorts of different types of trips are available to book at decent rates.

There's a few ATM's available in the area too, should you use this facility.

It's a 5-10min walk to the (boisterous of a night) end of the Strip and a lesiurely 20-30
mins walk to the (in my opinion) nicer, more couples/family orientated (Montechoro)
top end of the Strip.

Some places worth considering re accomodation...

Quinta Pedra Dos Bicos 4* apartments
(we stay here - book through private rentals though - usually MUCH cheaper)
Pedra Dos Bicos 4* Hotel (New last year)
Forte Da Oura Aparthotel
Oura Praia Aparthotel
Clube Praia Da Oura
Oura Estrella
Santa Eulalia Beach Club

Hope this is of some help.

Here here Milly Molly, the new town isn't just the strip, which some folks think it is, there are other nice areas to stay, eat & drink.