So for me, in this context given, they are very close and interchangeable. The slight nuance might be that "go" is a journey and "get" is the end result. But this is really a thin difference. I use "go to bed" more than "get". But look at this..."last night i went out and stayed out late. I didn't get to bed until 5am". Here, "get" adds the tiny bit of drama and emphasises the end result. But "go" would have been fine too.
In other examples..."After finishing work I go home. I usually get home around 7pm".
In terms of need a time expression - I would say, no, not at all. "After finishing work I go home. I usually get home really tired". Again, this is explaining the end state.