can i register my website to appear in google places in a place where my business isnt based and i dont have?

[Fredrik]

If I had a business in Northern Ireland and also the Republic of Ireland, I would probably have at least 2 domains. One .ie for Eire, and one .uk for Northern Ireland, and then put the .uk one in google places for Northern Ireland, and the .ie one for Eire.

Also, in order to do SEO, in order to get organic ranking, I am fairly certain it is easier to do separate pages for Eire, and NI. The sites can still have the same content, but focusing keywords etc to the local area where you are operating, in order to get better ranking.

As you have premises on both countries, there should not be an issue having each site be local to each busines premise.

I hope this helps.
/Fredrik