There are mostly three ways to drive into Ísafjörður. The first is from the ringroad in Hrutafjörður, and goes up north on the eastern part of the peninsula through road number 61. That way gives you the oportunity to stop in Holmavik among other places on the way.
The second way to get to Ísafjörður by car is by road 60 from the ringroad, 608 over the moor of Thorskafjardarheidi and then 61 through the many fjords on the way. In the summer, that is the shortest way from Reykjavik, but it is currently not accessible during wintertime.
Thirdly, you can take the ferry Baldur from Stykkisholmur to Reykjavik via the small towns on the western part of the peninsula. That way gives you a chance to see for example the great waterfall Dynjandi.
There are regular busses that go from June 1st to 31st August from Akureyri and Reykjavik. Information on that can be found on West Tours' homepage 
Additionally, there are two daily flights from Reykjavik with Air Iceland. The fare is relatively cheap if you just want to go from A to B.
The town is small, but the distances from the town to adjacent towns is further than walking distance. Thus, you would want to study the bus system that can take you all over, bring a bike or have a car. There is a bike rental in town for the active ones that don't want to walk around.
The Island Vigur is one of the most popular tourist destination near Ísafjörður.
Go hiking! The mountains are great all around. Check out the hiking map beforehand and get a printed one when you arrive .