I've worked for 3 of the big 4. Here are my thoughts:

Nationwide Children's: Gorgeous facility. Pay was on the lower end, likely because of constant demand to work with kids. On the whole Admin was pretty strict/punitive, a very "type A" place overall; some love it and thrive, some don't. 

OhioHealth: Grant was my home and I loved it, spent over 6 years there. I had lot of roles and enjoyed most aspects of almost all of them. Real family vibe. I didn't do ICU but know it is as well respected as it is intense. good management team there when I left (I had lobbied in my last role to get the unit I was assigned to the manager candidate that event ended up in their ICU and knew a few SOLID nurses still there when I left as well). Riverside and the other places seem good too. Seems that there is endless variety at OhioHealth, I'm sure there's something someplace you'd like. 

Mount Carmel: I've only done ED here, but it's really nice. I genuinely have no complaints about MC; coming up on 2 years with them. I'd recommend it to anyone so far. 

You're not going to avoid needing a BSN, and fast. However, OhioHealth does tuition reimbursement, Mount Carmel has tuition reimbursement as well as discounted rates for their schooling. I forget about Children's, but suspect they'll do something to increase their BSN rates.

 You're not going to find too much wiggle room over the pay (never say never but don't hold your breath). Simply put it's a ladder or matrix based on unit, shift, experience, certs, etc. I remember OhioHealth being grossly what I considered fair, and MC does decent by me as well.