Regular set of the "does not contain" kind
If a string doesn't contain $11$, then any $1$ is followed by $0$, unless it is the final $1$ in the string. Therefore you can break the string up into pieces of the forms $0,10,1$, the last one appearing only at the very end. This leads to the following regular expression for the set of binary strings excluding $11$:
$$ (0+10)^*(\epsilon+1). $$
If we furthermore want the string to end with $0$, then we have no terminal $1$. On the other hand, we also want to disallow the empty string. Altogether, we get
$$ (0+10)^+. $$
A similar case analysis leads to a regular expression for your language. Details left to you.