The only destination in Portugal which is served by direct flights from Belfast is Faro. Fare examples (using some of the cheapest available):
Out from Belfast International (with easyJet) at 1300 on Mon 14/09 = £67.49
Return from Faro at 1630 on Fri 18/09 = £130.49 (There aren't any September dates with cheap flights back).
Total = £207.98
Out from Belfast City (with Aer Lingus) at 0630 on Tue 08/09 = £89.99
Return from Faro at 1010 on Sat 12/09 = 91.99
Total = £181.98
NB: If you're travelling to the airport by public transport (or getting a lift, or you simply don't mind having to travel between the two airports to collect your car), there's nothing to prevent you flying out to Faro with one airline and back with the other. You might be able to get a lower total fare that way.
The (well-reviewed) Guest House São Filipe is very close to the bus and rail stations and charges £27.24 per night for a en-suite single room, making a total of £108.96 for your accommodation.
Even cheaper, at £18.92 per night for a single en-suite room, is Residencial Condado (which is also well-reviewed but accepts cash payments, not cards, only upon arrival), making a total of just £75.68 for your accommodation.
Both of those places were found on my favourite budget accommodation website:
http://www.hostelworld.com
(Don't be put off by the word 'hostel' in the title. Simply carry out a search for your requirements and then deselect 'hostels' from the filter, leaving 'hotels' and 'B&Bs' in place. I've used that site myself, to get a lovely room in a small hotel in Madrid for just €22 per night!).
Bus routes 14 & 16 can get you into Faro in just a few minutes.