You're embarking on an interesting journey!
There are direct trains but no direct flights for this journey. Catching a flight is the fastest way to do this journey. Direct trains are available as well. New Delhi (Delhi) to Shirdi (Maharashtra) distance is 1264 km and you can get there by flight + cab in just over 6 hours and 50 minutes. Going by train won't be that fast but you will get fares starting from ₹ 493.
Beautiful weather for sightseeing and other outdoor activity.