It does now look out of place among all the modern buildings. Anyone going to see it also needs to go in the Menger Hotel nearby. Lots of museum quality items from that era are on display.
When it was still open (it closed to the public a few years ago) the movie set for the original John Wayne movie, located on a ranch near Brackettville about 100 miles west of the real Alamo, had the chapel and many outbuildings recreated and it is surrounded by open ranch land so it looks very real and made you feel like you were standing in the 1800's.
In 1836, when the Alamo fell, the population for the area (now San Antonio) was 7000 people. Now it is about 1.5 million.