Cascais is one of the most popular beach towns near Lisbon and hence can be busy during summer. There are some funky shops and cafés lining the pedestrianised streets, which give the town a distinct beach vibe with a hint of swankiness. Cascais is a former Portuguese fishing village, so you'll still find plenty of seafood restaurants around, and it was a place the Portuguese royal family were rather fond of in the 20th century.
If you continue west along the coastline from Cascais you'll reach Boca do Inferno, the 'mouth of hell', where the Atlantic's powerful waves crash into a stone cave. It's a lovely walk with beautiful views, but don't set your expectations too high for Boca do Inferno itself. The show is most impressive in winter when the sea gets rough.
One of Lisbon's best surf spots can be found further north at Praia do Guincho.
If you head east, you can walk from Cascais to Estoril, which is where you'll find the largest casino in Europe (that's the answer you were looking for when you read my blog post Interesting facts about Portugal ;-) ). At high tide during winter the waves can be impressive as they smash over the concrete pathway between the two towns, so pay attention unless you want to cop a soaking (take it from someone who's been there, done that).
There is a train from Lisbon to Cascais, which leaves from the Cais do Sodré train station and takes around 45 minutes.