Mérida has the most Roman ruins of any town in Spain, so that is what you come to see. You won't be disappointed! A pass to see all the major sites is 15 euros. Talk about economical.
Teatro Romano y Anfiteatro- In my opinion, these two monuments are the most impressive of Mérida, and they do a fantastic job of presenting a lot of information in English. Both the theater and amphitheater are in excellent condition, and they are in the same location. If you are short on time, and only doing one day in Mérida I recommend you choose these as the sites you see. I have been to many ancient theaters all over Europe, but this one is special, and like I said, really comprehensive with the information.
Acueducto de los Milagros- Aqueduct of Miracles, is also in great condition and beautiful to look at. It's surrounded by a community park and another ancient Roman bridge, so it's a peaceful location. What I enjoyed most was watching the large birds build huge nests on top of the aqueduct. I believe they were storks. It added to the magic of the place.
Alcazaba of Mérida- A 9th century Muslim fortification part of the Unesco World Heritage List. The fortress has great views of the Puente Romano, and my favorite part was the Roman cistern, which is eerily quiet and dark, and filled with goldfish.
Museo Nacional de Arte- The building itself is a work of art, and it contains a vast collection of Roman mosaics, statues, and artifacts. A delightful experience, and it's free.
O'ribeiro- I stumbled upon this place. It's right across the street from the Alcazaba of Mérida, and it was packed with locals, so I thought I would give it a try. The seafood was fantastic. I had the mejillones (mussels), and the pulpo (octopus), and both were delicious. They don't seem to have a web presence, and there is a restaurant with a similar name that is not this restaurant that get's bad reviews, so talk about confusing. A great place for lunch after you visit the fortress. Here is a photo, so you know you are at the right place.
Nico Jiménez- This is where you go for the jamón, and they certainly know what they are doing. It melts in your mouth, and is the high level of jamón that Spain is known for. They are also the only place where you can try beer infused with jamón, or the only place I know about. Fun night! Great service too.
Entrecanas- A modern restaurant for fried fish and other tapas. They serve it with sauces too! If you are a person that lives in Spain you know that this is quite rare.
Let's be honest, Mérida is not the place you go to hang out. It's the place you go to experience amazing ruins and a town of mixed history; including Roman, Moorish, and Visigoth. I recommend you buy yourself a few bottles of wine for the room, and then wake up early and explore. Of course there are the typical Spanish restaurant/bars around the square where you can certainly have a drink, and I did find a few cool places too.
Mercado San Albín- A bullring turned into a gastro market? Yes Please! We were here a little early, so not a ton of places were open yet, but the space is fantastic. Antique memorabilia lined the walls, and local food is served.
La Piel del Oso- A great cafe to start your morning. It's a little bit out of the center, but right near Casa Mitreo, so a convenient place to start the journey of Roman ruins. You can get a latte here, and a good breakfast for a fair price.
Jazz Bar- This bar is everything you want; friendly service, cheap drinks, and good music. The atmosphere is comfortable and it's close to the center.
Hotel Mérida Palace- The hotel was clean, quiet, comfortable, and in a perfect location. The wifi worked, the shower worked, and it's in an old palace.
I'm not going to sugarcoat it for you; the train ride from Madrid to Mérida sucks. It's five hours on a local train with fluorescent lights and no bar car. Make sure you bring your own booze, snacks, and entertainment, and you will be good.