Stars are moving away from us...into what, infinity?

Einstein's static universe was empirically inadequate: it cannot account for the redshift data gathered by Edwin Hubble and others in the 1920s. The redshift data indicates that distant stars are moving away from us, and moving faster in direct proportion to their distance. Thus, the data indicate an expanding universe

The key characteristic of these models is that space is homogeneous, and hence isotropic (i.e. looks the same in all directions).