Caceres?

For Caceres will you have a car to park? That might make a difference on where you stay. Generally, though, I'd stay either within the "walled town" or just outside it around plaza Mayor or plaza de San Juan (this area is also "oldy worldy"). We stopped in the latter plaza at the NH hotel - a good hotel in a 16C building (with a public car park nearby) and only two minutes walk to the Arco de la Estrella which is the principal gateway into the official "old town". There may be self-guided walks available - there is a tourist information office - however we just "constructed" our own walk based on the Rough Guide to the town. It is an ideal town just to wander around enjoying the overall ambience of the streets and squares rather than there being any singular "wow" sight.

Badajoz might be worth a quick stop since you'll be passing. But personally, I'd carry on the extra 15 miles over the border to Elvas which is much more attractive.

yes we will have a car
Thanks for the suggestion of the alternate stop. sounds great

My wife and I are fond of the Spanish Paradores hotels. The one in Caceres is in a 14th century building and does offer paid parking. Some hotels in the city are in a restricted traffic zone, the Parador included, so check with the hotel you decide to reserve to find out where to park and if you can drive up to the hotel for check in. With the Parador, it asks for the vehicle registration number to ensure you don’t get a ticket. At other Paradors we’ve stayed at in restricted zones, e.g., Santillana Del Mar, Olite, Santo Domingo de la Calzada, access was limited to 30 minutes before the vehicle had to be moved. For a walking tour, like Nick, we select the places we want to see, then create our own walking tour.

I found the following link to a self-guided walking tour of Caceres: http://www.walkingextremadura.com/a-walk-in-a-renaissance-city.html
It also has walks for other parts of Extremadura, including Badajoz.
For Merida, Spain info has some good information on places to visit. https://www.spain.info/en/destination/merida/

Merida has some impressive Roman ruins and an archaeological museum with good mosaics (I don't remember the other displays). The city itself is otherwise not particularly distinctive compared to many other places in Spain.

Caceres is very interesting. I'm concerned that you will not be able to do it justice if you only have one night on a trip from Lisbon and make stops in both directions. ViaMichelin.com estimates the Lisbon-Caceres driving time (no stops, no traffic, no weather, no getting lost, no searching for parking) at 3 hr. 44 min. by the fastest route. Merida is off the direct route.

I'd probably skip the Parque Nacional de Monfragüe in December, while noted among birding enthusiasts, due to shorter daylight hours and considering many birds will have migrated south for the winter, there may not be much to see.

I agree with Acraven, with one night you will have just about enough time to see Cáceres‎, but if you add another night then you can consider using Cáceres‎ as a base to explore another site in Extremadura. You may consider Trujillo, a nice enough Baroque town and the home town of a few infamous Conquistadores. Or better yet, a day trip out to see the Real Monasterio de Guadalupe one of the finest religious buildings in Spain and a UNESCO World Heritage Site. Both within 1.5 hrs from Cáceres‎.

PS: It probably won't be cold enough (if at all) to snow in Extremadura until Jan/Feb.

I asked a similar question about a year ago, and got some pretty useful responses. Here is the link:

https://community.ricksteves.com/travel-forum/spain/have-you-been-to-caceres-and-or-merida

thank you for all the insight everyone