I am on an unrelated Board for U of H, but we were briefed a number of times on the Medical school and choosing the location was a tough, but very well consider decision. They seriously considered being in the Medical Center and even identified an available piece of land, but in the end the choice was to be near campus to reinforce the ties to the university.
As for the exact location and preserving the trees, I'm afraid that whole area will probably be developed over time. If you're not familiar with the U of H area, the campus is pretty hemmed in on the north by I-45, the east by the railroad tracks (with the exception of the Innovation Center (ex. Schlumberger facility) which is really a separate location) and the south by viable residential in University Oaks/Riverside Terrace. So I think that area of land to the southeast is destined to become part of the campus. There is political pressure from Third Ward leaders for U of H to not expand to the west as they feel that it would diminish the historically African American nature of the neighborhood. Plus TSU and Yates High School are right there on the border already. There is some room to expand to the north right up against I-45, but that land is currently serving as sports fields and personally I think that's a good idea as intramural sports add to the University experience and the mind boggling to me 6000+ students who live on-campus need recreation areas.