Udaipur is having lashing monsoon month. Called as land of lakes, from September it is one such ideal time to visit. Amritsar is having rainy season, though not much downpour is seen in coming week but you to do a weather check before travelling. November to March is an ideal time to travel. Both places have rains, my advice would be if you are a monsoon traveller kindly check the weather before travelling.
Dr .sheetal you didn't disclose from where you will start you planning for Amritsar or udaipur both places are beautiful & blissful
but for this monsoon season
I will pick udaipur. .. it looks quite beautiful in monsoon season. .. in your question you were asking about join you ? I can join you just share your starting point ? how you planning
like by train ,by car ,by bus etc . thanks & regards
September is good time to visit Udaipur, city of lakes. It's a beautiful place to visit with many places of tourist interests, breathtaking views of nature, mountains, lakes, palaces and also good place of shopping arcades. Udaipur is also an amazing city of various architectural historical forts like City palace, Lake palace, Saheliyan ki Badi, Chittorgarh Fort, Fateh Sagar, Etc.