Are search engines location specific?

Do search engines such as Google show you results that are closer to your location first or are results the same for every person searching no matter where they are located (inside of the same country)?

I can get my page at the top of results for 100's of keyword phrases but I cannot seem to get to the top when the name of the business city or city listed on the website isn't included at the end of the search term.

I.E. "Do This in Bradenton, fl"
opposed to
"Do this"

Is there a better way to get ranked higher for these search terms without the city at the end. I have Keywords in URL, anchors, title tags, meta descs and keywords, and the keyword spread randomly throughout the page. Thank you for any help

It depends on a ton of different parameters, but generally speaking, yes, search results are affected by your location. Although it does depend on what you're searching for.

As for your first question, search engines usually show location based results.

If you want to rank for a keyword with location attached to it then you need to build links with that keywords. Or maybe adding your listing to Google local etc might also help. If you have 100 links with anchor text "bakers" but if you have a competitor with two links "bakers in ABC" he is more likely to rank for "bakers in ABC" .