At present there are no hotels really near the Airport.
Your best bet would be one of the hotels at Parque de Nações or the Radisson Blu.
http://www.radissonblu.com/hotel-lisbon
These are all about 2 to 3 kms away. I doubt though they would do parking any cheaper than the Airport.
There is a hotel being built by the airport T1 but I have no idea when it will be open.
Addendum: I have just been informed that there is also a Holiday Inn Express in an Industrial area close to the Airport. Apparently there is an airport shuttle.
See: http://www.hiexpress.com/hotels/us/en/lisbon/lisap/hoteldetail
