We visited Dhaka for 3 days. Unfortunately we didn't have enough time to go outside the city. Assorted notes:
Dhaka airport was efficient and easy to navigate. No hassles, helpful smiling people processing our visas on arrival (USD50 + BDT7 each); on departure none of that boarding-pass-stamping and carry-on-baggage-tag-stamping that one encounters in India. Free fast wifi in departure area.
Drive between airport and Motijheel never took more than 50 min, even though both directions were on working days, 10am in one case and 1pm in the other. This is no guarantee that you will experience the same.
Purbani International was a perfectly acceptable hotel close to old Dhaka. A bit expensive, but paying for the higher-priced rooms gets you renovated, spick-and-span upper floor rooms with views over the bustling city. Good breakfast. Ask by e-mail and they will give you a 25-30% discount.
We stayed in the old city, and tried some 'name' restaurants. Hajir Biriyani was tiny and hugely crowded, you have to stand over others as they eat so you can grab their seats. The biriyani is quite mediocre, but everyone else believes it is great. Nana Miya's morog polao was better, but consists of some cold separately cooked chicken and tepid separately cooked sauce placed in top of hot rice. In general, biriyanis were not worth it for us, because we can't eat 10kg of rice at one sitting. It feels awful to waste rice in a country where many are hungry.
We really enjoyed eating at Al-Razzaque. Attentive waiter trying his best to make thing good for the foreigner (cleaning the dishes and glasses, finding forks and napkins....) but doing it quite sincerely, not as a pitch for a bigger tip. Excellent food, low prices.
Of course there is nothing world-class to see in Dhaka, but we enjoyed the boat ride, and also our visit to Ahsan Manzil. The people from the National Museum have done their best to turn this mansion into an interesting site, with informative displays and captions, although marred by some really bad English. The Armenian church was also very interesting---we were shown around by an articulate and well-informed young man who said he was the son of the caretaker.
It will not be news to anyone that we found Bangladeshis to be very pleasant, courteous and welcoming without ever being overly attentive, never staring or being pushy the way people sometimes do in India. I speak Bengali, and it is just wonderful to be somewhere where it is the lingua franca, so to speak. There was much less "Benglish" than in Kolkata, but a lot of Dhaka dialect. Not difficult to follow however.

