Not to be a dream crusher, but you'll just have to take the job that hires you. You may be able to get into your area of choice right away, but if not, don't be disheartened. You can work your way into that area or you may decide you like the area in which you start. If you enjoy the fast-paced traumas, then you would enjoy a setting like ER, but you said you also like to continue in their care; if that's the case, then you may enjoy NTICU.
I work in a MSICU, and while we do get critically ill, unstable patients, most are not unstable, but are critical, stable (but that can and does change in a moment at times). Then, others are more intermediate ICU patients, but we don't have an intermediate ICU, so they hang with us until stable enough for the floor. It really is a variety, and what I have learned in my time there, is that I enjoy caring for the oncology patients (both terminal and those with a good prognosis), so in the future (not looking to leave ICU anytime soon), I will do oncology nursing and hopefully research, as well. I enjoy this unit, though, and feel I am able to make a difference in my patient's outcome during my shift. Point being: you'll probably end up in different nursing roles/units during your time as a nurse. Start somewhere, and see where that takes you.
Best of luck to you!