The entire area around UNM Hospital, and indeed UNM itself, is safe and considered a very desirable area to live. The closest neighborhoods to the hospital area, and ones in which you'll find a lot of doctors, lawyers, professors, etc. living, are Summit Park, North Campus and Netherwood Park.
That entire area is usually referred to as the North Campus area, since it lies directly east and north of the UNM North Campus, which is where the university's health sciences and law facilities are located. The North Campus lies directly north of Lomas Boulevard from the main UNM campus.
Another area close-by is the Spruce Park neighborhood to the west of the main UNM campus and directly south of Lomas from the area where the UNM Cancer Center is located, both west of University Boulevard and east of I-25.
On the east side of the main UNM Campus and southeast of where UNM Hospital is located are the Monte Vista and College View neighborhoods. These neighborhoods lead into the Nob Hill area on Central Avenue, which is a very desirable and hip area filled with small shops, restaurants, etc.
And further east from the North Campus neighborhoods you have the Altura and McDuffie Park areas and neighborhoods, which also have lots of doctors, professors, etc. from UNM living there. These areas are centered on Washington Street and Constitution Avenue.
Somewhat further out from the hospital area you have the University Heights and Silver Hill neighborhoods which lie directly south of Central Avenue from the Main Campus of UNM. Of all the areas around UNM and UNM Hospital the one which can seem somewhat sketchy is this area.
Overall it's pretty safe and nice, but there've been incidents lately and in recent years that give the impression of the area being unsafe. Two rather high-profile incidents both occurred at the 7-Eleven on University and Central. The most recent one involved a man who got into a fight at the store and was chased down an alley in the area and shot and killed by the police. The most notorious incident happened a couple of years ago when a group of people robbed the 7-Eleven and actually killed a clerk who worked there.
This area, though, is one which has seen an awful lot of revitalization and renewal in recent years, so the neighborhoods are definitely on the rise rather than in a decline. This area also happens to be the most affordable of the areas near UNM and offers lots of affordable apartments and rental homes. It is sometimes referred to as the Student Ghetto for this reason. It has a more youthful vibe and is seen as being hip and somewhat edgy. That's opposed to the other areas which are seen more as places where the UNM faculty and graduate students, etc. live and which are more sedate in their nature.
Here's a map on Google to help you see more clearly the areas and neighborhoods I describe around UNM Hospital:
https://maps.google.com/maps?q=unm+h...15000&t=h&z=15