I got 350 in the BITSAT & 3606 in the JEE Advanced. I'm sure I will be getting CSE in NIT Trichy under the home state quota. Which one should I choose BITS Goa, Hyderabad, NIT Trichy, IIT Bhubaneshwar

If you are eligible for all the above-mentioned colleges then BITS Goa and NIT Trichy are two of the best options. 

BITS Goa offers Computer Science with a total fee of 14.7 lakhs. Last year, the college scored a placement record of above 90% with the highest CTC of 56 LPA in the CS department. The cut-off last year for CSE was 352 so you may get selected. 

BITS Hyderabad offers the same course with a course fee of  15.66 lakhs. The cut-off last year was 342. The IT companies offered an average salary of 14 LPA in last year’s campus placement.

NIT Trichy offers CSE with a course fee of 5.72 lakhs, so there is one advantage of qualifying for an NIT in India. The cut-off rank for JEE Main lies between  280-5317 at this institute. The CSE branch had 100% placement last year with it being the highest recruiting branch for the past 3 years in the college. 

IIT Bhubaneswar offers CSE at a fee of 7.91 lakhs, and the JEE Advanced closing cut-off was between 1246-4068. The CSE branch had 100% placement with salaries ranging between 10-35 LPA in 2019 placement. 

IIT Dhanbad charges a fee of 8.91 lakhs and the cut-off for JEE Advanced rank lies from 1619-5657. In 2019 campus placement, 90% of CSE students were placed and the maximum salary offered was around 40 LPA.

So after comparing all the colleges, NIT Trichy is the best option.