I got AIR 2380(CRL- 19k) in GEN-EWS category, Can I get core branch(CSE preferred)in good NITs ??

According to cutoff of previous ranking you can go for following nits. Below nits cutoff for general category -

NITs                          other state closing ranking                                           (computer)

Nit mizoram                   37003

Nit agartala                     19209

Nit silchar                        18956

Nit arunachal Pradesh     29596

Nit meghalaya                    33237

You can also apply for iiits, gftis. There are likely chances to get above nits . To know cutoff for iiits and nits view the below link -

https://engineering.careers360.com

Well you are correct that this is the first time for EWS category and it is really hard to predict how much advantage that will bring to you. However I feel that maybe you can get admission in institutes where you would have needed atleast 12000-13000 rank in crl. So maybe try to shortlist such institutes from the previous year cut-offs. Also you should fill out all the possible choices and not just those which you think you can get cause you never know! Some probable colleges for you might be

1) NIT Raipur CSE/IT

2) NIT Durgapur

3) IIIT Jabalpur

4) NIT Patna

5) IIEST Shibpur

6) BIT Mesra IT

Do not just stick with the NITs since many IIITs and GFTIs are also doing really well in terms of placements and also the facilities which they provide to their students!