Planning to visit next week, would love to visit Ajmer as I heard that there's more greenery over there.

I am from south and I would like to visit rajasthan. I am weak in Hindi but understand thoda.What all precautions to be done ? Also I have not made arrangements for stay and accomodation, it's a solo trip as well. I heard of Ajmer and people over there. Admired by the stories and can't wait to visit. I am not planning for desert visit but if possible hiking a mountain for a misty morning. Will be only coming between 10-14 of Jan and staying for a week. I never loved any state by hearing the stories from my friends who travelled to Rajasthan. ❤️😍 Edit: suggest me the best places to visit so I can plan accordingly as I have not booked the tickets yet.