You can go to Kutch from Ahmedabad via bus. But the major city nearby Kutch is Bhuj. For roaming, you can visit Kutch museum, Kutch sanctuary, Great Rann of Kutch. In Bhuj, you can visit Mandvi beach and go for city shopping. Have a nice trip.
I've been Kutch in January. you can catch train or bus from Ahmedabad to Bhuj. while stay at Bhuj and visit local sightseeing like Prague mahel and Aina mahel, Heera baug, bhujodi village, Swaminarayan Mandir. day two, Mata no madh, koteshwar shiv mandir and Narayan sarovar. it's a route around 320 kms. day three, visit Kalo dungar and white Rann in evening. Mandvi beach is also there. and zero point border, you can visit but permit should be taken at Bhuj before going to white Rann. (prior a day or two.) also Dhola vira sight and gudkhar sanctuary is there but distance matters. so major destinations covered in three days.for more information, you can visit my blog on tripoto. Kutch nahi dekha to kuch nahi dekha. https://www.tripoto.com/trip/kutch-nahi-dekha-to-kuch-nahi-dekha-5c459a0c8ffe6?ref=mobwapp&source=awp
Hi yoganand, You can have bus from ahemdabad to bhuj . Bhuj is the city in kutch. in bhuj you can visit few places 1. Amisar lake
2. Ayna mahal
3. Kutch Museum
4.Swaminarayan Temple If you have time thn goto white desert from bhuj . explore desert and festival. From white dessert you can either goto a mandvi beach or kado dungar (Black hills) . Come back to bhuj from there and take bus or train to ahemdabad. In ahemdabad you can visit heritage of ahemdabad and monuments . During your trip in gujarat you can stay in haveli take a look on the below link for more details of haveli https://www.tripoto.com/trip/stay-in-heritage-haveli-instead-of-hotels-during-your-trip-to-ahemdabad-5c59576ca0de2?ref=mobwapp&source=awp