Adobe's Fireworks is the way I usually do something like that. Essentially what you'd do is cut the map up into a grid of small images that then fit back together in a table. Each cell in the table is a link to either a web page or a pop-up. You can also have ti make roll-over replacement images, so you can do things like cause buildings to highlight when the user points at them. Fireworks will make the slices, allow you to configure the behavior, and export a web page all on its own. All you'd have to do then would be to make the target pages.

The disadvantage is that you can only make rectangular slices. Well, that and Fireworks is Adobe software, and thus currently only available through their Creative Cloud subscription. However, if you think you can learn the software and get your job done within 30 days, you can take advantage of the trial version: https://creative.adobe.com/products/fireworks