Wow! I'm going to ditto what Tiki said. Great, descriptive post! You've described my hospital to a "T".
In our hospital, we've got three nurseries and do not really have a Mother/Baby system due to lack of interest from the parents (our hospital demographic generally prefers to send the babies to the nursery and keep them there until discharge, or they will keep the babies for a few hours in-room then send them back).
IMO, the Well-Baby nsy is probably the place where you will get the most time to cuddle or hold the babies, though, as someone else mentioned, they need their rest. Working a true Mother/Baby unit, you'd not only be taking care of the babies in-room for the most part, but you'd also be nursing their moms who are recovering during the PP period. Our WB nsy gets VERY busy, so with 6-8 babies per nurse, there is a lot of work to get done, though they do have down time (especially at night) during which the nurses can hold some of the babies.
Our Level II and III nurseries are exactly as Tiki described. In our Level II, we have AMPLE opportunity to hold the babies, not only during feedings but also because some of them (particularly those who have stepped down from Level III and were on vents for extended periods of time) are extremely fussy and hard to soothe. Also, those step-down babies need to be taught about non-medical touch (about 90% of their time in a Level III is medically-related, invasive types of touch), so we do make a special effort to massage, cuddle, soothe, and talk to these infants. I LOVE working in the Level II nursery for that reason. Most of the major medical hurdles have been jumped, so it's all about increasing health and preparing for discharge.
Our Level III does get infants that can be held, but for the most part, these babies are SICK and that, coupled with the fact that a nursery can get extremely noisy with the alarms and staff and whatnot, means that they need as much rest as possible. However, if you read about kangaroo care at all, you'll find that sometimes babies actually do sleep better when they're being held (due to the comfort, warmth, movement of your breathing chest, and heartbeat). We get some babies in Level III who are in Isolation rooms and get virtually no contact other than from the nurse who is assigned to them that day, and who may have 1-2 other infants to care for. I like to make a particular effort to hold them and interact with them in a soothing, non-stimulating way whenever I can. Some of the nurses don't like doing Isolation, but I just love it, especially when the babies are on minor O2 or on room air and can be "handled." Our Level III also gets babies who have certain genetic disorders (Down's Syndrome, etc.) who don't require O2 but may have heart problems (or babies who experience things like SVT's) who can be cuddled and held. So I wouldn't say that in a Level III you never get to hold babies; I certainly do as much as possible, because I feel that comforting touch is essential for the well-being of these children.
For me, I also enjoy our Level III (we get floated between the two nurseries depending on need or request) because even the vented babies need tender care. I was scared of the Level III at first because I was intimidated by the status of these tiny babies, and the machines they were dependant on, but after a while, I came to look forward to the nights when I would be assigned a particularly ill or difficult baby, because I knew that SOMETHING I did would be important, whether it was just cooing to the baby or gently stroking a limb or cheek, or performing oral care, or whatever. You'd be surprised how those ELBW's can react to a little TLC.
In this area, you have a few actual Level III's, then a whole lot of Level II's (in the smaller, private hospitals, they will often call their Level II's NICU's, though in fact most of their babies are feeder-grower's, along with a few stable vents), and every hospital has either a Well-Baby nursery or a Mother-Baby system in place. You just have to explore the opportunities at each and every hospital until you find one that's a perfect match for you.
Wherever you go, I wish you the best of luck. Come by the NICU forum sometime- they have some wonderful nurses who frequent that forum who I owe a debt of gratitude to.
Let us know what you decide!