Westlake is a neighborhood, as you no doubt surmised, on the western shores of a lake – central Seattle's Lake Union, to be specific. This is a dense area but doesn't have much of a community feel.
While there are a good number of amenities, it's not particularly exciting and you won't find much nightlife or shopping. However, Westlake is centrally located so you're only minutes away from great options in adjacent neighborhoods.
Thanks to the boom in neighboring South Lake Union there is increasing residential development here. For housing take your pick from single-family homes, condos, townhomes, apartments, and even houseboats (including the one from Sleepless in Seattle). Parking can be difficult here so to avoid the daily hassle of cruising the streets looking for a spot, make sure your home comes with parking.
Downtown Seattle: 2 miles / 10-20 minutes by car / 20 minutes by transit
Bellevue: 13 miles / 25-40 minutes by car / 80 minutes by transit
Redmond: 15 miles / 20-45 minutes by car / 50-60 minutes by transit