When was the last time you stayed in Graca? This part has change the last 18 months with lots of galleries, Urban kitchens )Senhor Do Monte is packed with food trucks... etc. Its considered one of the happening parts of Lisbon... the best restaurants are here (Damas is the happening club - opened 10 months ago)and Martim Moniz (Topo Bar etc) and especially Largo Intendente is only 4 minutes walk down..
As first time visitor I wouldn't recommend to stay where you along the Cascais train... nothing wrong with that part... BUT its too expensive - especially these days with the music festivals... And you 'miss' the Lisbon feel if you're not in walking distance from your hotel (or metro) - have tried it myself... one more thing - its school holiday - the beaches are packed with kids arriving in buses (just got back )....
Any way - just wanted to post a very fresh update on this one...
If you want to go to the beaches the ones around Costa Caparica are much better - and as easy to reach as