This page shows the best observability of 4-Vesta over the next few months. The graph will show the time of culmination (highest altitude) unless this would be during daylight, in which case the height shown is at dusk or dawn. Hover over a point to see the time and date. Note that asteroid orbits are perturbed by Jupiter in particular and so data is unlikely to be reliable more than 100 days in the future.
Note: the data are for a central UK location. To adjust for your location see advice here.