Most major hotels will have at least one restaurant open throughout the day. The
iftar meals, to break the fast at sunset, are a highlight -- five-star hotels have huge, festive buffets, followed by
suhour meals throughout the night. Last year I enjoyed the iftar at the Shangi-La on Skeikh Zayed Road, the year before that at the Sheraton Dubai Creek, both of which were outstanding.
The malls and large shopping areas will be open; some smaller shops will not be.
Most places do not serve alcohol at all during the month.

I am not sure if there are exceptions; there might not be.