So if I were you, I'd start building up the EF to $5-10K... perhaps save for your trip at the same time... and then start saving for renovations, up your retirement contributions, etc. once you have a decent EF.
Actually what DH & I ended up doing was putting most of our savings into one account. We had a set amount that wasn't to be touched except for emergencies, but amounts above $X could be used for multiple purposes (like large purchases, or your trip and renovations). We kept increasing the reserve amount until we had plenty for emergencies. Structuring your savings like that might be something to consider too, since you have multiple short-term savings goals.