Can I prefer AIIMS Patna over IGMC Shimla considering Patna as a city in Bihar?

Yes, AIIMS Patna is definitely a better choice than IGMC Shimla because no matter how much natural beauty you will experience in Shimla, being a state college you will have the disadvantage of bonds. 

AIIMS Patna on the other hand is an institute of National Importance that has been growing leaps and bounds over the past 11 years. The best part is that these new AIIMS are expected to grow more in the future while the state colleges maintain a similar situation. 

AIIMS Patna will offer the best facilities and infrastructure and you will be guided by the best faculty. AIIMS Patna has a much more diverse student body than state colleges and the experience will be surreal as you are a part of the group. So I feel if you are against Patna because of the city or location, trust me as a medical student you will have no time to explore the city, and mostly your day will be spent inside the campus. So why miss the AIIMS tag!