Stay Smarter
Tell the hotel to organize an auto for you the previous night because finding transport at 3 am can be quite stressful if not pre-booked. That is, if you are planning to go for the famous Bhasma Aarti at 4 am.
Shoe Storage: Temples do not allow footwear inside. Remove your fancy branded shoes, leave them safely at the hotel, and wear simple flip-flops(chappals) which can be easily removed and stored at the temple counter.
Do not even think of trying to drive your car up to the temple gates; traffic restrictions are that strict. Leave it parked at your hotel and jump on one of the thousands of cheap Totos or electric rickshaws which can ply through narrow lanes and by-lanes.
Try the Thali: Don't order à la carte every time. Try the "Malwa Thali" at the hotel or nearby restaurants to taste the local Dal Bafla (a regional variation of Dal Baati), which is a must-try culinary experience in Ujjain.
April to June in Ujjain is burning hot. Make sure your room has AC, not just a cooled one but explicitly confirmed as an AC room. The hotel's air conditioning works well; however, it becomes m andatory during these months.