How are you doing settling in from your move? We've relocated several times for my DH's job (hence my screen name) and I cannot get excited about going away for a vacation right after a move either. I've done enough packing and unpacking and attempting to care for my children without being able to find their stuff!
We've done staycations right after moves and really enjoyed them. Its worked well when in a place that is really different and interesting. You could also add an overnight to someplace near -- are you 3 hours or so away from something cool? Our best staycation was one when we had moved close enough to go to the ocean for an overnight, but hadn't managed to do so yet.
If you can't stand the thought of PLANNING a vacation but are fine on actually going on one, put your DH in charge of planning. I suspect that this defaults to being your job, a heck of a lot of other stuff does, too. Most people have no clue what it means to move such small children so far, including the daddies (especially if you have no support network in your new city). Have him do more, you guys may need to readjust what is his job and what is your job for a while.
Consider an all inclusive vacation. We did one and I honestly think it was the only REAL vacation I've had since we had kids. Most of the time, I feel like I'm still doing everything I normally do but with more obstacles. The all inclusive vacation was very relaxing and restorative *for me*. Everybody else had a good time too. (We are considering an all inclusive for this summer).