Let me start saying that Dhaka, and Bangladesh in general is not a place in which you can easily move on your own. We were fortunate in discovering Deshghuri for being our guides in our Bengali adventure.
We hired the tour company for the entire week that we have been in the country, but I'll focus in Dhaka since this is a "Dhaka Day tour review".
What a chaotic city! Went there with my girlfriend and we have loved the experience of visiting and having a glance of the city, but we would not choose it for staying in a long term.
First week of October was still too hot to enjoy being outdoors, always above 30 degrees Celsius, and high humidity. According to what the guides said, November to January would be the best in terms of weather conditions. Most of the time we passed in an A/C car that the tour have arranged for us, going to one place or another. We have also tried the rickshaw for visiting Old Dhaka.
Distance to scenic spots are not large, but due to poor street conditions, narrow streets and traffic jam you can take hours to arrive to your destination.
What I liked the most was actually the atmosphere of the city, the people, kids, more than any touristic spot in Dhaka.
There we have visited the Lalbagh Fort in Old Dhaka (deserve a visit), Panam City (deserve a visit), the Pink Palace, which is now a museum, it worth if you have some time to kill, is located just next to the Port of Dhaka at the Buriganga River (not sure if is the major port).
We passed by the Parlament, I later regretted not to stop and make some pictures at it.
Mr Sajjat, owner of the tour company, who speaks perfect English, is very kind and polite, he has knowledge about his country, and also Mr. Pavel, also a great guy, they were very helpful the whole trip. We got some stomachache from they 3 to day 7... and they managed to get us some light food (actually we just ate white rice for almost 4 days), took us to a local clinic while in Khulna, and were sincerely concerned about our situation. Due to this I don't have places which I would recommend to eat. We tried an italian at Gulshan neighbourhood (La Forchetta) wasn't that good. Star Kabab (local kababs chain) were recommended on this site, but I personally didn't like much.
I loved the food that was served to us during our 3 days trip to Sundarbans. But probably there, in our last meal my gf and me got intoxicated with something, maybe the water, maybe the oil... Tasty fish, lentils, bbq chicken, rice, nan and similar bread, etc etc were delicious. Get ready to eat using only your right hand ! (anyway the guides arrange fork and knife if you don't want to use your hands, they never push you to do something that you may don't like).
In 7 days I probably saw 5-6 mosquitos, nothing to worry about, but anyway bring repellent with you. Also is better if you dress according to their dress code, they are a "moderate" muslim country, my gf only in sacred places covered her hair, nothing bad happened, normal people stare at you just because they are very curious.
Expect to hear many "how are you?" and "which is your country?" in the street.
Bangladesh is a country that still has a long path/way to go, very undeveloped and with huge difference between the few but powerful richs and the rest of the people.
Tourism is also undeveloped, but with the company of capable guides and the respect for local customs and traditions, this should be a great experience.