I'll second Siteground. My WordPress sites were gradually getting slower on DreamHost - with support saying there weren't any problems. I switched to Siteground a few months ago, and so far, I've been happy with them.

Siteground had a "move my WordPress site" plugin that worked much smoother than I expected.

That plugin is probably based on BlogVault's Migrate Guru, which is available for free and works with a number or hosts. It's a game changer, really.