Which university has a better EE course: IIT Mandi, IIT Jodhpur, IIT Patna, or ISM Dhanbad?

My knowledge is limited to IIT Patna as my brother was a student of the same and thus my answer talks about that particular institute only. Firstly, judging an IIT on the basis of its location is not logical. What matters is the job opportunities and facilities it has to offer. In that sense, IIT Patna will definitely serve you well. 

IIT Patna offers one of the best UG EE Courses. For an undergraduate student, EE is one of the most challenging branches. But the plethora of opportunities it has to offer makes it a more lucrative branch too. IIT Patna EE branch includes courses from both Electrical and Electronics leaving you to decide on which field to pursue.

If you are inclined to CS and coding stuff, you can do it despite being in the EE department. IIT Patna has one of the best coders, a senior of the EE Branch who cleared Google Code Jam and was also part of this year’s ACM-ICPC Team which qualified for World Finals and Secured 56 Rank. Another senior cleared GSoC which is quite an achievement.

If you are a research enthusiast and want to go for a Master's, then IIT Patna is the best place. Its highly supportive professors help you in every way. The seniors are helpful and guide you in making the wisest decisions.

It’s best to talk to the students of all the institutes you mentioned and then decide.