I am staying in a hotel long term and have 2 stove top burners but no oven. How do I cook a 2.14lb pork loin fillet without the oven?

Obviously, you can't bake it or roast it without an oven.
You could slice it into "medallions" and fry them in a pan.
Or you could consider buying a crock pot or slow-cooker?

You could also use a covered pot (or Dutch oven) on the stove top and do a pot roast! All recipes – complete resource for recipes and cooking tips (http://www.allrecipes.com) always has lots of good ideas.