It's been reported that Cleveland was in love with Rashaad Penny and were likely going to take him at 33. Maybe that's why they were comfortable passing on Saquon Barkley. Regardless, they're in the market for a RB and starting off Day 2, they will likely take one early. There's no fear that the Giants will take a RB in between the Browns first 2 picks, so they could take him at 35 if they feel like they have a higher rated guy for 33.
My prediction is:
1 (33) Josh Jackson/Isaiah Oliver: Just because the Browns took Denzel Ward doesn't mean they're finished overhauling what was an atrocious secondary last year. Josh Jackson had a solid year at Iowa and played great against Ohio St., which shows he can shine against strong competition. Both Oliver and Jackson are bigger but slower than Ward, so they can be a slightly different kind of corner, possibly covering some of the taller WRs. Poor Ward will likely start out with an assignment on the best wide receiver in football, Antonio Brown. He might be able to keep up, but he's likely going to get schooled.
2 (35) Nick Chubb/Derrius Guice/Ronald Jones: I would personally prefer Nick Chubb if I were picking, but I'm not so suffice it to say the Browns will take a RB after the Giants take Will Hernandez.
3 (64) Orlando Brown/Shaquem Griffin/Eqanimeous St. Brown: All 3 of these players would fill a need for the Browns. I think Griffin is the longest shot to actually go in the second round, as I'd think he'd go in rds 5-7. However, I watched him play and the dude is a baller. If he's a gamble as the 5th player you take in the draft, I'd argue he's worth it. Orlando Brown had a terrible combine, but he plays the game well. I think he could fit here and it'd be cool to reunite him with Baker. St. Brown is a fantastic WR who I think is being undervalued in this whole process. I hope that he doesn't fall out of second round.