Coimbatore

Apply on the website (preferred course) or go there and then get the admission.

Yes, you can easily get into it.

Here are some colleges based on your percentile for MCA:
1. PSGR Krishnammal College for Women, TANCET Cutoff - 71 percentile.
2. Dr. GR Damodaran College Of Science - [GRDCS], Coimbatore TANCET Cutoff - 68 percentile.
3. Government Arts College (Autonomous), TANCET Cutoff - 61 percentile.
4. HICAS, TANCET Cutoff - 71 percentile.

The fee structure will be less compared to private institutions. The fee will be around 6000 Rupees year for the computer engineering. The course fee will be less if you get a seat through the entrance test conducted by the government. If you didn't secure the seat through the entrance exam, the fee will be high because the government will not provide any fee reimbursement. The other expenses like your food and accommodation will be taken care by yourself.

This is the link of this PSG College Coimbatore for B.Tech:
https://www.shiksha.com/college/psgct-Coimbatore-19398.