Courtesy of another poster, you might want to use this resource and look up BME, as it is not the sort of thing offered everywhere:
https://public.tableau.com/app/profile/jonboeckenstedt/viz/BachelorsDegreesAwardedin2022/Dashboard1
Biochemistry is tricky because it can be a concentration rather than a major, or go by different names. But I believe all the colleges I name below have both available in at least some form.
OK, so smaller colleges, urban, and BME is going to be a tough combination.
One (popular) idea would be Pitt, which is not really small but at least not too big, strong in Bioengineering (with various tracks) and Biochemistry, and in a great location in a cool city. Your fields are also very big at Case Western, which is medium-sized and in Cleveland. Rochester in the city of the same name, also medium-sized. Marquette in Milwaukee, again medium-sized. Delaware is in a college town, Newark, but very easy to get into Philadelphia. Drexel is in Philadelphia.
Boston University is a leader in BME–tough admit because it is in the Boston area, but still might be a good choice for a reach. CMU, also in Pittsburgh, tough admit just because it is a very highly-ranked school. WUSTL, in St Louis, again a tough admit just in general. Rice in Houston, same deal. Hopkins and Penn, obviously very tough admits.
So those are some ideas I think worth checking out.