This really depends on your definition of astronaut. The Google definition is:
a person who is trained to travel in a spacecraft.
I'd suggest that the first person ever trained to travel in a spacecraft never actually flew. Again this depends on your definition of training though I suppose.
However I fear this isn't the answer you're looking for. If you're definition is the first man into space then we're talking about Yuri Gagarin, at 324.9 km apogee.
Interestingly if you type "yuri gagarin altitude" into Google it tells you his height - either that or he flew a very low spacecraft at some point. Put together the two facts from this answer and what do you have? Nonsense!. :)
The following apogee altitudes are in kilometres. They are ordered by launch date.
Vostok 1 324.9 (Gagarin)
Mercury 3 187.5 (Shepard, suborbital)
Mercury 4 190.31 (Grissom, suborbital)
Vostok 2 244 (Titov)
Mercury 6 265 (Glenn)
Mercury 7 260 (Carpenter)
Vostok 3 218 (Nikolayev)
Vostok 4 211 (Popovich)
Mercury 8 283 (Schirra)
Mercury 9 267 (Cooper)