Of course it all depends on where you go and when you go and where you stay.. If the number you came up with scares you, then Think about taking the kids someplace else for a totally different experience ... and this year, not next.....
Lets say a winter wonderland Christmas and New Year Trip to Central Europe for the snow (maybe), Christmas Markets, Lights, Food, Concerts and Theaters.
Friday 21, Last day of school
Saturday 22 Depart IAH
Sunday 23 Arrive, night 1 in Budapest
Monday 24 night 2, Budapest
Tuesday 25 night 30, Budapest
Wednesday 26 night 4, Budapest to Prague by CSA Flight ($125 each or $500) - Christmas in Prague
Thursday 27 night 5, Prague
Friday 28 night 6, Prague
Saturday 29 night 7, Prague
Sunday 30 night 8, Prague to Vienna by train (about 19 euro each or about $85)
Monday 31, night 9, Vienna for New Year's Eve
Tuesday 1. night 10, Vienna
Wednesday 2. night 11, Vienna
Thursday 3. night 12, Vienna to Budapest train to Budapest (about 19 euro each or about $85)
Friday 4, night 13, Budapest
Saturday 5, night 14, Budapest
Sunday 6, Flight Home
Monday 7, Home
Tuesday 8, First day of school
International Airfare: December 22 to January 6 (your kids Christmas Break) Houston to Budapest is about $1200 round trip on Turkish Air; so $4800.00
European Airfare Budapest to Prague is about $125 on CSA, so $500 total. Why not an open Jaw into Budapest and out of Prague? Best i could find, this was cheaper x 4 is a lot.
A short term apartment rental for four can be had for under $125 a night. If you found rooms for 4 at $175 in a hotel; well done!. But with the short term rental you can probably get at least two bedrooms in one apartment. This trip is 14 nights at $125 or $1,750.00. The schedule has minimum 3 night stays that most short term rentals will require.
Food? Hey you have an apartment. Eat breakfast in. For this trip, i figure $120 a day for basic good food (I think your number is low for where you plan to go) = $1680.00
Train tickets $170 (by them in advance and buy them from the train company not a broker)
Tickets and other costs, $100 a day. I think thats a pretty fair guesstimate including transit tickets. So $1400
So, my total for a trip this Christmas is $10,300; and i would call that $11,000 or $12,000 with all the incidentals overlooked like taxis to and from the airports and those special shopping trips along the way.
Ive done this trip with my kids, and at Christmas. Actually we have spend a number of Christmas' in central Europe.