Sylhet is my hometown, although I left at 9 and am a little estranged.
Here are some nice places that I discovered (or rediscovered):
a) Area around parjatan motel - nice spot, lots of nice views from a hill top on Airport road
b) Shahjalal University - pretty campus about 10 km N of town
c) Zakaria Resort - near Khadimnagar, a hilltop resort with 360 views and entertainment park including ferris wheel and toy train
d) Hazrat Shahjalal's tomb - he was an amazing holy man, worth a visit if you are religious
e) MC College (aka Sylhet Govt College) another nice campus
f) Forest Dept Land - some nice forests on north-east side of town, near Baluchar. There was a picnic spot but it may have shut down.
g) Tea gardens - Lakkatura and Malnichhara are very close to town. Bicycling possible on the trails (though I have not tried it.)
If you like shopping, Manipuri patterned saris etc in Police Line.
In summary, places just a little on the outskirts are nice. Avoid the center, specially Zindabazar and Bandar, unless you like crowds and traffic jams.
One view from top of Zakaria Resort:
View to the East from Zakaria:
Stadium under construction near Lakkatura:
What tractors were really made for:
Another type of Lilly: