Mathura is relegious place as you know but if i've to go for solo trip i'd select jaipur. Its so fascinating rajasthani cuisine and dresses i'd love to try hawelis and colorful streets and so big mansions and especially architecture in jaipur is nothing less than an ancient film set.
Depends on the month you choose. The weather in Jaipur is pleasant between October- to- February. And during Holi will be the best time to visit Mathura.
Jaipur would be better. I have been to jaipur and mathura both. If you want religious visit then go for mathura and if you want historic visit then go for Jaipur. plan according to your preferred type of visit and also considering budget. Happy planning..!! Happy journey ..!!
Jaipur is the best option if you are going in the month of January.. by that time you can go to the Jaipur literature fest also.. it may be start on 21st January.. thank you..