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In this case, the primary objective is a good user experience. Send to relevant page. A link to the homepage would be great, but even a deeper link it is still a link to your domain, so be happy with that and start planning your next program!

Image maps present links in a very standardized way that the search engines definitely index so it's more of a question of how you want your information presented in results. If I'm presenting a cluster of results for a barbershop search in a local area with an image map, I wouldn't want that broken up until it got to the individual page for a specific location, as one example. As for the alternate text tag, it's the same "alt" so it'll be read the same way.  A good practice for usability, regardless.