CACERES, SAPIN. As much as I would recommend a trip to Mérida of Extremadura for the history lover, I would recommend a trip to Cáceres for students, who also take an interest in history. The reason why is that it is a place with historical significance and a fun nightlife, affordable by those on a budget.
I myself went with my study abroad trip, so my hotel expense was paid for by my tuition in the program, and we stayed at the Hotel Don Manuel. It is a 4-star hotel located within walking distance of the Plaza Mayor of this small town, and I would highly recommend it. It has a very modern feel, high-speed wifi, and beds built by angels. It looks like Booking.com has a deal where it costs 55 Euros/night to stay here. A little pricey, but not much more expensive than 2-star hostels in Cáceres, which run about 30 Euros/night (e.g. H2 Cáceres), so if you are looking to spend a nice weekend getaway in Extremadura, both would be viable options. Additionally, on this link I see options for other high-rated hotels in the area around 10 Euros/night cheaper than Hotel Don Manuel, so those might be good options as well.
As for the history of Cáceres, my trip provided us with a tour guide, which was very helpful. However, the city is very beautiful at night, and many of the historical sites are located in close proximity to each other, so one could certainly enjoy a self-guided tour just as much if not more than a guided tour. A few of my favorite buildings were San Francisco Javier Church, Co-Catedral de Santa María, and the chemin de ronde. One of my favorite parts was visiting the Museum of Cáceres. With free admission, in it lies an ancient Moorish cistern that is still in tact, along with some ancient, inscribed stones. Again, coming to Extremadura one can expect to see a lot of history, as that is its main appeal. However, the food and nightlife are quite nice in Cáceres.
My study abroad group took us to dinner Saturday night at La Parilla de Galarza, which was phenomenal. The menú de la casa, priced at 26 Euros, included appetizers of jamón iberico, chorizo, salchichón, and scalloped potatoes, followed by all the meat you can eat. Eating with a big group equates to a good discount, so I would recommend this restaurant for that. I certainly did not leave hungry; if you are not looking for such a big meal or not looking to eat with a large group, this place also has decently-sized entrées to share, costing around 10-15 Euros apiece. For the student on more of a budget, La Cacharreria is highly recommended online as a place with an authentic Mediterranean feel, and good tapas priced around 4-5 Euros.
Of course I had to check out the nightlife too. Not quite as noisy as Madrid or any other big city, but I had quite a bit of fun in Cáceres. The Plaza is replete with bars, offering good music and moderately-priced drinks. Copas ran between 4-5 Euros. I would recommend checking out Berlin Rock Bar located at Plaza Mayor 21 in Cáceres, as well as the few bars surrounding it. The eastern corner of the plaza is where all the fun is, and I found myself popping in and out of 3 bars in that direction. Cáceres is a fun little city, and for the student looking to see the history of Extremadura while still hoping to taste the nightlife, I would recommend spending the night in Cáceres. Much bigger than Mérida and Trujillo, young people are sure to find a way to entertain themselves in Cáceres.