It is unlikely that you will find anything cheap in the b&b range near Lisbon Airport - Just a few airport type hotels.
I would recommend the Hotel IBIS Malhoa which is well situated for the Sete Rios and Praça de Espanha Metro Stations (6 -7 minutes walk) and is easily accesible by taxi from the Airport. There rates are currently Euros 55 per night for a double room. They are clean.
We often stay there when we drive up from the Algarve.
Note there is no metro link yet to Lisbon Airport. I do not recommend the buses unless you are in the know (like me! :) ) There is an airport bus to down town but I'm not sure that is where you will find the right mix of accomodation. Taxis are relatively cheap in Lisbon.
