Seville, Granada, and Cordoba vs. Valencia

Hi! I'm looking for some input as I figure out how to plan a trip for the first time (but do have experience traveling). I'm planning a trip to Spain in January, with the current plan to fly in and out of Madrid. I was thinking I'd spend about 4 days in Madrid to have time for day trips and then spend about 5-6 days in some combination of Seville, Granada, and Cordoba. I keep seeing people on here say that Valencia is wonderful and now I'm wondering if I should ditch Southern Spain to do Madrid and Valencia (or maybe also Barcelona)? I generally am a city person but believe I would also love southern Spain and the slower pace.

Appreciate any and all input, thank you!