Below is a list of the methods I've used in the past to build traffic to new niche sites very quickly. I'm hoping some experienced Warriors and traffic experts can chime in and let me know if they still work and, if possible, which methods are even better...
Very Low Competition "Long Tail" Search Phrases -- Choose several (10+) long tail keywords that have very little competition in Google and build pages around them. Use short, unique, decent-quality content and one or two optimized images (and, if it makes sense, an embedded YouTube video). Make sure the on-page SEO is perfect and ping the search engines.
YouTube Videos -- Create short optimized videos around medium and high search volume keyword phrases. Build lots of free or low-cost backlinks to the video URLs. Promote your niche site in the videos and link to it at least once in the description areas. Possibly pay a few bucks to get some initial views and shares.
Pinterest -- Create interesting, high-quality images and add them to pages on your site. Create a new Pinterest account and "Pin" all the photos from your site. Create boards with your photos and other related photos that catch people's attention. Optimize everything as you go for your main keywords.
Facebook Pages -- Create a dedicated Facebook page for your site. Add great photos and some unique content. Promote the page (using Twitter, Pinterest, YouTube, etc) to get friends and followers. Possibly pay a few bucks for some initial friends/followers.
Web 2.0 Pages -- Create optimized pages on popular web 2.0 sites like Squidoo, Hubpages, Tumblr, Webs.com, WordPress.com, etc. Use unique, decent quality content so they don't get taken down. Link to your niche site several times in the content, including at least one large "Click Here!" graphic.
Guest Posting -- Find sites/blogs that accept guest posts and send them a couple quality articles with links to your new site.
I know there are several other good methods for fast traffic. Please let me know what I'm missing. Thanks!