I am starting a new website for a local business and have entries listed for it on places like urbanspoon, yelp, google+ local, etc. I am thinking of listing these citation sites on my business website to encourage visitors of my site to go and review the business on those sites. If I dofollow I will pass link juice to my page on that site, but doesn't that mean that the very very little PR juice I have will be leached away from me? Is it better to nofollow them?
The practice of hoarding "link juice" isn't a valid practice anymore. Google got wise to the whole "PageRank sculpting" game and amended their algorithm accordingly. Any PR that would have passed via a given link, were it not nofollowed, is effectively thrown away.
The only likely exception to this is where users are able to post unmoderated links, for example via blog comments or forum posts. In those cases, where there's a risk of someone linking to something nasty that you don't want your site associated with, nofollow is a wise precaution.
More broadly, attempts to manipulate search ranking inevitably backfire sooner or later. As well as fighting spam and hardcore "black hat" SEO, Google also takes issue with "over-optimisation", i.e. doing too much to tweak your site for search. Focus on quality in design, code, server configuration and content, and you won't go far wrong.
If you dofollow the link a part link juice would leak out to the other site (depending on how your site is built, this part can be small or "quite big").
You definitely would not lose all the PR, but I would nofollow them if I were in you.