jitaruvictor

I'm not going to get into the flights department as I would be partial to Qatar Airways. So, I'll get to the next part of the question: If you are set on western hotel chains, than I read some very good advice above. However, I stayed in many places in Dubai and only once in one of those hotels. It;s true that it's not my style. I prefer smaller hotels, as close to local traditions as possible: In that idea, I would recommend Comfort Inn Deira. It's a nice hotel, close to the metro station (it's much better than taxi or uber, especially during rush hours). There are several supermarkets in the area and they offer free shuttle to Al Mamzar beach (a great place for families). If you really want a hotel chain, I'd go for Ibis - much better prices and excellent services. There are lots of Ibis hotels in Dubai for you to choose from (I stayed at Al Rigga). Since you mentioned small restaurants, let me recommend you a place in the Al Rigga district (very close to Ibis Al Rigga Hotel) - Sandwich Club. It's a medium size terrace on the sidewalk serving cheap and delicious traditional Arabic food with awesome lemon mint (mint lemonade). I ate there several times and brought friends. Every time, it was great.
The attractions aren't expensive... of course, depending on what you want to do. Burj Khalifa can be visited for approx 150 USD pp I think, the aquapark at Atlantis the Palm in approx 60-70 USD pp... I don't think there are attractions much more expensive. For your kid, don't forget about the kids area in the Dubai Mall and Mall of The Emirates...it's fantastic (not even for children)...In both malls, the kids areas are on the last floor.
As far as getting to the Palm area, there is the nice option of taking the Hop on Hop off bus or public transport (but you have to change metro, bus, tram and the monorail), but if you want a more direct approach take a taxi... it's easier if it's not rush hour.
If you want more about Dubai, I have lots more info on my blog. victorjitaru.com/dubai
All the best and, if you want to know more, either check my blog or ask away.
Happy trails!