If you're downtown, to get to Ballard by bus take the RapidRide D line or the 15. Get off just after the Ballard Bridge to explore the local breweries.
For IPA's, I recommend Reuben's Brews. Adam is always experimenting but has some solid regulars. I'm fond of Hale's Supergoose, but it's not the most outstanding IPA you'll run into. Populuxe is also does well with IPA, often has them on cask and/or dry hopped; I love their their CDA/BIPA so much I (unsuccessfully) tried to clone it, though some find it a bit on the roasty side.
Or, make it easy on yourself and head to Ballard Beer Company (which is a taphouse) or Chuck's Hop Shop.
In the nearby Fremont neighborhood, hit up Fremont Brewing. They have an excellent line-up, IPA and otherwise. Fremont and Reuben's are my favorite Seattle breweries. There are several bus lines that go through Fremont, get on board in Ballard or downtown.
When it comes to Seattle IPA otherwise, I think of Elysian, Schooner Exact, and Two Beers.