My daughter and I stayed two nights in Esslingen last December, 2023. We went to the Esslingen market the first evening, and went back the next morning. We had originally planned to also see the Stuttgart market, but we were having such a good time in Esslingen we decided it was not worth the bother. The Esslingen medieval market is fantastic, especially for fans of the middle ages. There is also a lovely and not insignificant "regular" market right next to the medieval market (complete with a Käthe Wolfahrt pop-up and decorated roofs.) In addition, there was a handcrafts market, weekends only, which we enjoyed. For a break, we walked outside the market area and "discovered" the Esslingen castle right there. We were sorry we did not have more time to explore it. Esslingen is a nice little city.
Also, I had trained in to Stuttgart to meet my daughter at the airport. The Hbf is a huge construction zone, and the city area around it was not at all inviting. I questioned wanting to go through there at night. I had been staying in the nearby town of Ehningen and the hotel clerk warned against Stuttgart at night, it's not as safe as the small towns. He also recommended the Esslingen markets over Stuttgart's, saying that while Stuttgart was the biggest, it was also more commercial.
In Esslingen we stayed very near by the market at the Eco Inn, a clean, comfortable and economic choice with a very good and very substantial breakfast, and a very doable walk to/from the train station. For dinner, we took a break and ate at Weinstube Kleine Traube, which I highly recommend. The best schnitzel (their speciality) I ever ate. Reservations are highly recommended that time of year; the only drawback is that you have to make them by telephone. After dinner we enjoyed another flaming evening at the medieval market.
While I do not recommend against the Stuttgart Weihnachtsmarkt and hope to get there some day, with the time we had (and considering jet lag) staying the day in Esslingen was the right choice for us. I admit that we prefer an "enjoy" pace as opposed to a more frantic "see as many things as possible" pace.
Have a wonderful trip!