Alexandria is a perfectly safe area. However, I'd keep going further down. The traffic below DC can be pretty bad heading south and it would be better to get through it on your first day.
I'd go just a little more south to get out of Alexandria .... Woodbridge / Dale City is home to Potomac Mills mall ... you'll find plenty of rooms and food options and probably be past the worst of the DC traffic (exits 156 and 158) http://www.simon.com/mall/potomac-mills/about
OR, look at the Lorton area .... see the forum about the autotrain and recommendations for rooms and food. Lorton is between Alexandria and Woodbridge.
(I worked in Alexandria for 6 years, and lived in Woodbridge; Alex' as safe but the closer you are to DC the worse the traffic and higher the prices))
Living in the DC area I would say Woodbridge area where Potomac Mills is a much better stopping point than Alexandria due to Lower Prices for rooms. The Hyatt near the airport averages $179 a night and the bad Hilton there is $149 a night typically. Woodbridge would be about $100 a night. That's a significant savings on the average family vacation budget.
I might even try to push on to Fredericksburg if time allows. Gets you completely out of the traffic and should be even cheaper. But traffic from Alexandria to Fredericksburg is highly unpredictable. You can make in less than an hour if you are incredibly lucky but I have had it take 3 hours. So I think it will come down to timing. Lorton or Woodbridge would be perfectly safe.
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