I went to Andalusia last year mid January with my mom and it was great. We only had 8 nights and since we really wanted to focus on Andalusia we cut Madrid from the itinerary completely and flew into Malaga (via LAX to Heathrow) instead of a direct flight from LA to Madrid and then a train. We rented a car so it was more of a road trip.
We stayed in Ronda, Cordoba, Granada and right by the airport in Malaga (late flight in and super early flight out so it was really convenient). Long story short, Malaga and Granada seemed the most lively with the most people out and about in the evening. Unfortunately we didn’t go to Seville. That said, there were still plenty of places open in the evening in Ronda and Córdoba (I’m thinking of restaurants mainly) and plenty to do during the day, however, on this trip we tended to get up super early and not stay up terribly late.
I went to Arles a few years ago in October and wandered around the old town for quite awhile one midweek night trying to find where all the people disappeared to and where the open restaurants where! We eventuality found them but everyone seemed to all be in the same square!
If you only have 8 days (7 nights?) I’d maybe just stick to Madrid and one other place and really experience them. Maybe a day trip or overnight to Toledo added in? I regret not going to Toledo (and not bringing a warmer coat!) but really tried not to do toooo much even though it’s tempting. Also, the weather was great during the day but ended up being a bit colder than expected at night. Quite a bit colder actually. Whatever you choose it will be amazing! We loved Spain so much we are planning another trip soon!