I don't know your definition of ''decent'' but the Pensao Praça da Figueira‎ (Figueira Square Pension), located just about 1000 feet away from Castelo de São Jorge, sounds decent enough to me:

"Benefiting from an excellent and privileged location, the Pension Praça da Figueira is located in Lisbon’s historic area of Baixa Pombalina. The client will find, less than 50 metres from the hostel’s main entrance, all public transportations and car parks.

Lisbon is a city full of attractions for all tastes and ages. The main ones are near the Pensão Figueira, as the Figueira Square, the Santa Justa Lift and the quarters of Alfama and Bairro Alto.

To visit Lisbon – whose origin comes from the name Ulisses – is to get to know a truly historical city. So in a simple stroll along the streets near the Pension Figueira, hosts have the opportunity to know a great part of the city’s history, its beautiful monuments as well to discover the great cultural and gastronomic diversity of the typical quarters of Lisbon and the downtown shopping district.

The Praça da Figueira Pension occupies a restored building, in the historical part of the city.

This pension is place where everyone is welcome. Our collaboraters speak english, french and other languages.Recomendations:- Lonely Planet.

- Rough Guides.
- Routart.
- Petit Futé.
- Time Out.

To offer an even more pleasant stay to its clients, the Pensão Figueira offers some services, among which:

- Enjoy the welcoming of the friendly staff.
- Reception open 24 hours.
- Towels.
- Credit cards accepted.
- Luggage storage.
- Foreign currencies exchange into Euros.
- Internet access.
- Telephone/Fax Facilities.
- Laundry service.
- Rent a car information.
- Tourist information.
- Tickets and information about the best tours around Lisboa.
- Breakfast not included.
- You can catch the tourist bus just in front of the pension ( Praça da Figueira).

Option 1:
Rooms with bathroom (+ dryer) heating and TV.
Single room, double, twin or triple.
Prices range from € 23.75 to € 28.75 per person / day.
Single from € 37.50 to € 47.50 per day.

Option 2:
Rooms with private shower, washbasin and TV.
Double or Twin rooms (with double bed).
Prices range from € 18.75 to € 23.75 per person / day.
Single from € 27.50 to € 37.50 per day.

Option 3:
Rooms with shared bathroom.
Room for one, two, three or four people.
Prices range from € 13.75 to € 17.75 per person / day.
Single from € 17.50 to € 27.50 per day.

Option 4:
Suite with 3 single beds + living room with sofa bed (2 people)
Equipped with 2 TV.s, air conditioning, telephone, bathroom. Complete and microwave.
Prices range from € 22 to € 39 per person per day, depending on the number of people."

€1 = $1.3387. 1 euro is about 1 and one third dollars right now.

Map, courtesy of Google Maps

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If this isn't good enough for you, please let me know what you mean by "decent." I can guarantee that I will find the most suitable place for you. I'm not going to lie, nothing motivates me more than a generous tip.

Boa viagem!

I lived in Lisbon and I do not recall any budget hotels that are decent enough within the Castelo of São Jorge. I can only recommend one hotel which is the Tivoli Jardim (Gradens Of Tivoli) which is located 10 meters off in the main avenue of center lisbon (Av de Liberdade). This is relatively close to the Castelo area and a frined of mine has been there and he liked it. Apparently, according to their website you can get as much as 53% discount depending of course on certain conditions, such as length of stay, etc. This period is relatively low peak so you should be able to get a decent rate (for the average rates applied). Here is the website of Tivoli Jardim:

http://www.tivolijardimhotel.com/

Good luck.

How many euros/night are you willing to spend? The Vip Executive Suites Marquês‎ is 78.50/night

Casa costa do Castelo is at least 85/night.

Sete Colinas Hotel has rooms starting at 64/night.