Vilanova is situated just off the strip approx 50 metres, not an hotel though, its self catering
http://www.vilanovaresort.com. Solar de Sao Joao situated just off the strip, nice little complex, again self catering. Be careful if you check the latter one out as there are another two complexes with similar names, dont get them mixed up.
Dom Pancho, self catering, situated just off Estrada St Eulalia, approx 500metres from the strip, but in an area with plenty bars & restaurants.
Soldioro, self catering situated at the bottom end of the strip just past Wild & Co bar, 200 mtres from the beach. As Glynis says travel republic are one of the cheapest booking agents, also have a look at
http://www.freedomdirect.co.uk it will come up on webpage as Heys travel,
http://www.hotelopia.co.uk
If you want a hotel try Hotel Aldeia, situated directly on the strip so you could suffer loud music, people shouting etc from the bars facing, not my choice but lots of folks like this place.