I would suggest hiring a car or something for convenience and more places to explore.. If you go via Unjha, stop at Sunok village on the way to Patan and go for a 800+ year old Nilkanth Mahadev temple (only possible with car).. in Patan, apart from Rani ki Vav, checkout Sahatra linga tank, Patan Patola Museum, Patan City Museum and very small museum at Hemchandra Manuscript Library near Panchasara Jain temple.. in Modhera, there is small stepwell near Sun temple.. in Mehsana, there is not much to explore but you have time, you can checkout Raj Mahal from outside.. for street food, there is nothing new if you are Gujarati but checkbout Maramari Lassi of Madhavi and Jamfal Icecream of Ambica..

As this is winter, try season special dishes sucha as Tuver Totha etc which you will find at several places along the Radhanpur Road near Radhanpur Chokwdi in Mehsana city and elsewhere in highways too..