Biresh Vrajlal said
1 year, 5 months ago: Defo a tough one but it takes time. I manage Tune Hotels’ FB page. we’re a budget chain of hotels. I started the page 3 years ago and over that time, have organically grown the page to over 40K likes. Not much but its a captive audience. The following is what I did to build it:
1. Invite your friends to like first (its a social network)2. Email your guest database to like the page (tell them its because they’ll get special offers and other tips & info)3. Share little known facts about the destination/location4. Advise them on moneysaving tips when they travel, share content from lonely planet/frommers/travel blogs, etc.
5. Do FB only promotions
6. Do mini contests with giveaways
7. Joke sometimes, ask questions, create a poll, quotes, etc.
8. Share videos from Youtube in respect of location, events, things to do9. Offer special partner deals and announce exclusively on FB10. Take pics of guests when they check-in and share them on FB page (especially if its their anniversary, birthday, etc.)
Be personable, show that you care, always give value and forget about comments and likes, they will come on their own, but first focus on giving value.
Also, a prominent link on your website inviting guests to like your FB page would help as well 
Hope the above helps