Fly to Lisbon and take the Metro to the train station at Cais do Sodre. (you need to change from the Red Line to the Green Line at Alameda) It will cost 1.50 euros for the journey plus 0.50 euros for the card ticket (which is reloadable). At the train station you can use the same card to get your train ticket which, to Monte Estoril, this will cost 2.75 euros. So the total journey will cost 4.75 euros (including the ticket).
I stayed at the Estoril Eden (4 star). Probably not the best hotel around and not the most up to date. But it cost me £56 per night for a double room including breakfast and a sea view. There are 2 pools one indoors, the other outside. It sits up a hill and gives good views over the sea. I've added a couple of time-lapse videos from my balcony to show what you could get.
There are also photographs taken in the Estoril and Cascais areas. All within walking distance of the hotel.
Please look at Daisy I's Weekend trip to Lisbon post (below) as it is all within the area.