Okay, so everyone else must vacation differently than I do, 'cuz I think $2000 is a perfectly reasonable budget. Granted, I tend to go low-budget, 'cuz I'd rather have a picnic in Paris than a spa day and 4-star steak dinner in Fort Worth.
The big question is: $2000 to cover how many people? Just the two of you? And how old is Ava? Then, what kind of vacation are you looking for? City? beach? mountains? Are you open to camping? Youth hostels? (you don't have to be 20-something for these--they have family bedrooms!) Do you have local connections anywhere that can help you out (e.g., I once rented a chalet in Switzerland for $600/wk from the uncle of a friend). What time period are you thinking of? There are some great deals for overseas flights these days, into early fall. You have to be flexible with dates, however, to get the good deals--being willing to fly on Tuesdays or Wednesdays is a big plus.
A couple of examples of cheap vacations I've done, of various scales:
1) Last summer, me + DH + 1-yr-old DD went to the Sunflower River Blues and Gospel Festival in Clarksdale, MS, and had a GREAT time. Entire cost for whole trip for 3 people (we roadtripped and packed a cooler for picnics): $500
2) Pre-baby, I did a long-weekend snowboard trip to Switzerland for $1000--found a hot-deal last-minute flight for $500 including taxes, stayed in cheap hotels, ate out of the grocery store, and spent priceless days on the slopes....
3) Also once did 6 weeks in Europe on $3000, including airfare and tuition for a one-month Italian class in Siena.
So cheap travelling you can do--the further you go, the more creative you need to get to keep airfare low--and some options become less attractive with a little one (wouldn't camp on the beach in Italy with a 2-year-old, for example, since it's too noisy to sleep until about 10pm...) PM me with more about what you're looking for, if you want more specific tips...