Bagerhat

Local buses run from Khulna regularly (Tk 30, 45 minutes). It's also connected to Mongla with only slightly more effort.

A cycle-rickshaw from the bus stand to the Shait Gumbad Mosque should run around Tk 10.

Unless you're in a hurry, you may want to just walk to the sights from the bus stand. Head west along the main road, a fairly nice walk save for the speedy honking buses. The first sight you'll come to is the dargah; start asking around for it after about 5 km or so. Shait Gumbad is another 2 km or so west along the main road from the dargah turnoff.

• 1 Shait Gumbad Mosque.
  Literally meaning the "Mosque of 60 domes", it's slightly misnamed as it actually has 77. It was built in 1549, and is one of the country's best mosques. While it's not un-interesting, if you've seen any mosque in India, Pakistan, Iran, or Afghanistan from this period you'll be pretty underwhelmed. Worse is that foreigners are charged to see the mosque which is nearly sacrilegious. Don't expect the grumpy staff to let you into the museum if you visit around lunchtime, and yes, you'll still have to pay to see the mosque even if you skip the museum. Tk 50, including admission to the onsite museum (museum open 08:00-12:00 and 14:00-17:00). 
• 2 Mazar Khan Jahan Ali. The tomb of Khan Jahan Ali is a major pilgrimage site in the area, and hundreds of visitors stop here daily to pay their respects to one of the country's more famous holy men. It's south of the main road and about 4 km from the bus station. As with most dargahs the tomb is covered in colorful cloth, and women must pay their respects from the courtyard outside. 

There are several other mosques along or just off the main road along the 5-km stretch west of the bus stand. Most are single domed and peaceful but not all that interesting unless you have a specific interest in mosques of this style and period.

The only options are some basic dhabas near the bus stand and near the dargah that serve the standards. - you may want to do a quick health inspection of the food before deciding on one.

There isn't much to buy here aside from some prayer beads and other little trinkets near the dargah.

There's a couple of lackluster budget hotels just north of the bus stand near the river. There isn't much reason to stay the night here as the sights can be visited within an hour or two and Khulna and Mongla are both so close. If you must stay, pick one and it'll likely run around Tk 50-70 for a single or Tk 120 for a double.