The domain name and hosting play a part – putting a registered office address on the page or all of the pages wil localize your site as well however the only thing that will rank you is good quality relevant content .
It matters not where a page is hosted if your site is not going to rank.
If you get to the stage where you are ranking well and you are looking to localize you can always use subdomains hosted in those particular areas . A little bit more expensive but there you go .
Three years ago i was buying .co.uk domains left right and centre and i had people telling me i was crazy as it was a worthless domain . Now whose laughing . The domain carries weight but content is king
Regards
Greg