From Patna Junction, the best way is to just book a cab to Gandhi Maidan. Instead of going towards the bus depot here, you will find IIT Patna buses outside, board one of them. It will take around 3 hours to reach IIT Patna.

From Patna railways get down at Danapur railway station and wait for the bus. I think it will take less time to reach the IIT Patna campus. The timings of these buses are available on the IIT Patna website.

The people of this city are very approachable and will guide you. 

IIT Patna hostels have double occupancy rooms in the first year. A typical room of a first-year student at IIT Patna has

• 4–5 shelves with an inbuilt almirah
• Two beds
• Study table
• Chair

You can get your room cleaned by the helpers on your floor. Every floor has two lavatories that are cleaned at least twice every day. IIT Patna maintains a hygienic environment to ensure the good health of its students and a healthy learning environment. Rooms can be changed after permission from the warden. Single occupancy rooms are allotted in exceptional cases though you will be missing out on some major fun. 

This is what a room of a first-year student at IIT Patna looks like.

Make sure you enjoy the shared rooms in the first year because you will be getting single rooms in the second or third year. 

Awesome is indeed the right word to describe IIT Patna. It has managed to grow at an exponential rate despite being a new IIT and establishing its own name. Here are a few things regarding the institute that make it awesome

• The institute has many GSOCers every year and IIT Patna also participated in the World Finals ACM ICPC. 
• The placement scenario here is great and the average packages of CSE and EE are as high as INR 35.57 LPA and INR 24.85 LPA respectively.
• IIT Patna has a good coding culture and organizes its own open-source coding event called NWOC, Njack Winter of Code. Students are exposed to various projects right from the 1st month of 1 st semester. Competitions like Robowars or Death Race challenge the students' knowledge.
• IIT Patna has a very hardworking student body that conducts weekly classes of competitive coding, app development, web development, etc.
• Hosca, the House of socio-cultural activities, enhances the cultural environment by promoting dance, drama, music, etc.
• There is a good bond between juniors and seniors and ragging is strictly prohibited.

The list is not exhaustive and you will find many aspects of IIT Patna that make it the awesome institute it is. 

The Electrical Engineering department of IIT Patna is well-regarded and is considered more rigorous than other branches. However, the opportunities provided are plentiful. Here are a few pros and cons of joining the institute.

Pros

1. Being new it has excellent labs with modern instruments.
2. The alumni are very helpful although the network is not that elaborate.
3. The seniors are very cooperative here and are a blessing for the juniors.
4. Some of the professors here reach you so well that you end up falling in love with the subject.
5. IIT Patna EE average package is INR 24.85 LPA, the highest is INR 82.05 LPA and the median is INR 22.23 LPA. The placement scenario is great with around 83.56% placements.

Cons

1. The number of PSU companies is very less.
2. Jobs in core sectors are very less and more in software companies. 
3. One of the toughest and most challenging branches.

I think IIT Patna EE is a good choice given that you are interested in the branch.

Yes, the new IITs like Goa, Patna, etc provide good future prospects. However, you would like to consider these points.

• Don’t go for the new IITs that don't operate from their permanent campuses as infrastructure and facilities play an important role in enhancing your academic environment.
• You will face lesser competition in the new IITs during placements and the companies visiting are almost similar to the old IITs. Thus new IITs increase your chances of making it into a good company.
• Old IITs enjoy a good prestige and thus have better ties with foreign universities thus making it easy to get LORs to do foreign internships or higher studies. 
• Old IITs are better for girls because the rules in new IITs are not well established and are in the developing stage so girls usually face a lot of restrictions here.

Now it is up to you to decide