Which are the good colleges for MBA / PGDM with good placements within a budget of 5 lacs including hostel and mess facility?

You can try for NIT. There are very few government colleges, which accept MAT score. You can also go for PUMBA. If you can write TANCET, then PSGIM would cost you Rs.4 lakhs.

RIIM is not a good option. Last year, I visited the campus and it's too compact and average salary package is next to being okay.

The fee structure of RIIM, Pune is 7 lakh rupees.

You should get admission in RIIM, Pune. You can pursue MBA along with a certification course in 5 lakh rupees. The maximum fee would be 5,50,000 rupees.

SMS, Varanasi and Lucknow are the best options for you. They have good placement assistance too.