Here's my opinion as well as what I know.
St. Jude is $24 on nights, so I think days is around 18-19. They have a 2 to one ratio or maybe it's 4 to one, but in any case the ratio is supposed to be good and it is a good place to work. I went for a tour of St Jude and the atmosphere is wonderful. Sorry I don't know exact info.
The best pay is Baptist, but they also have a rep for mean nurses and high nurse ratios. This means 8-10 on days and 15 on nights. Now I did clinicals there and I didn't find the nurses to be mean or rude, but that's my opinion. Oh yeah, the pay is $22 on days and with shift diffs, night weekends the pay is $30. Don't know the specific shift diffs, but someone answered that question on one of these TN threads. Don't think new grads start in ICU and they have a waiting list for weekend only or it's a year of experience required (not sure which), but it's like $45 an hour.
Methodist is ok for environment. The pay is $20 on days and if you are an extern prior to graduation, you get an extra dollar. They may have increased though.
Nurse patient ratio on the telemetry floor I worked on was 4-5 to 1. Sometimes it was 6, but not usually. Methodist has weekend option. I think all the hospitals do.
LeBonheur is the childrens hospital associated with Methodist and I was told that the pay is a little higher. They have an intern program that's 16-20 weeks for new graduates and yes you can start in their NICU or PICU.
St. Francis is my favorite and they have 9-12 month internships for most areas, but there is rumor of the OB unit closing. Pay is 20.60 a hour with benefits and 29.50 with out. I work there as a nurse tech and I find the atmosphere to be very welcoming.
The MED you can start in the NICU and the ICU. They are a level 1 trauma center and they do have new grads in the ICU, but the orientation is 3 months and I don't know is that's long enough, but people do it, so I guess it is. Not positive about the pay, but it's over 20, I think.
The VA I have no clue about pay, but they do have an extern program.
I'm sorry If I have been vague, but I gave you the info as best I know. I've done clinicals at almost all the hospitals or work there except for the VA. To me your best bet is LeBonheur or St. Francis for environment, ratios, and experience.
PM me if you have more questions.