I scored 496 in NEET 2019 (my first attempt), and am from West Bengal (UR). Would it be better to drop and prepare again for NEET 2020?

Hey,
It entirely depends upon your calling. If you feel that dropping a year will help you prepare better and you can ace NEET with good marks,then go for it but if you are planning on dropping a year for the sake ot anyone else,then Don't. As you go through lots of emotional ups and downs when you take a drop because the family members start expecting a lot from you.
See,now coming to your present score,you will get a government Medical College under State Quota,so I would suggest you to go for it.
I am providing below the link to the article of the previous year cutoff of NEET in West Bengal that will help you know about your chances in any Medical College in a more specified way:
https://medicine.careers360.com/articles/neet-cutoff-west-bengal
Hope this helps.
Good luck.

Dear Sir / Ma'm, since you have not mentioned your category, we could not come up with the list of probable colleges. However it will be advisable if you get a college even in the mop up round, do take admission. No on eknows what will be the conditions next year and how much difficult the paper will be. So, if you manage to get any government college, take admission.