If you want to travel and dine for free, the best way is to start a travel blog. Obviously the more professional and the bigger your blog is, the better hotels you will get. You can get a few free options such as hosted WordPress or if you invest a little bit, a self hosted WordPress site which would look more professional. Traveh.com offers a professional free travel blog that you can also use.
1. Be a Travel Blogger
Hotels are suckers for good reviews. Most hotels would do almost anything to get people to talk about them, if you take nice photos, that's an even bigger plus point. Photography is an expensive project and you would be surprised to know, most hotels do not refresh their photography often enough. In reality you are not getting the room for free. You will need to do a review of the hotel and it's facilities and because it's free, you are obligated to say only the nice things. Depending on how well you negotiate, you can probably get 2 nights for free and a couple of free meals at the hotel.
I've witnessed how stupid some hotels are by giving a full board experience for free to TripAdvisor reviewers because he / she was a Senior Contributor. This is not allowed under TripAdvisor's traveler review guidelines. Bloggers get away with it because of what little knowledge hoteliers know about digital. No offense to the conventional marketing guys, but they shouldn't be doing anything with a dot com.
Here's a pro tip for hoteliers: When using a blogger, make sure you get proper keyword back-links to your website and that photos are tagged correctly. This ensures that not only do you get eyeballs from the blog site, you get some SEO points on search engines as well.
2. Be an Asshole of a Guest
This is exactly what you need to be, an asshole. Complain about anything and everything. The first time around you will probably get compensated with a free stay, free dining and a free and fast airport transfer because the hotel couldn't wait to get rid of you.
This method isn't without its risks. You would have to pay for the rooms first, then risk the hotel not giving you anything for free. You also run the risk of getting blacklisted from certain hotels.