you don't mention tyres ? and typically a vibration in this speed range is down to the wheel / tyres being out of balance, so it can easily be resolved by any tyre retailier
However the vibration could also be the following
Tyre defect - any cracks or bulges on the side-wall of the tyre (inside and outside) these will throw the tyre out of shape and produce vibration - take a good look over the tyre sidewalls and bear in mind that anything that looks suspect when static will probably be ballooning out and far worse at speed so if any doubt then replace the tyre. Also check if the tyres have been fitted the right way round as some types are directional
One other thing to check for which isn't covered by a balance check is out of round or bent wheels, if you use a dial gauge on the axle to measure the run out on the wheel rim this will ensure that the wheels are round and true
Worn suspension joints - jack the car up so the wheel is off the ground (you’ll need to do this for all 4 corners) and shake the tyre from top to bottom and from side to side (with someone holding the steering wheel on the front) there should be no play in either direction. Any play in 1 direction will usually require a joint to be replaced, if there’s play in both directions then the wheel bearing may be at fault. If theres play only up and down its the strut top mount - to find this one you have to shake the suspension strut it self up and down with the wheel off the ground - so you may need to remove the wheel to check this one.
Now with the car jacked up on that side with the wheel about 2 inches off the ground use a steel bar under the wheel and lever the wheel up and down slightly, you should be able to look at the end of the axle and see if the suspension arm is moving up and down separately to the axle.If so replace the bush
To feel if there's a worn strut top bearing then lightly hold the spring by hand and have your assistant move the steering from left to right with the wheel on the ground - a worn bearing will feel 'notchy' through the spring. The wheel needs to be on the ground for the test to load up the bearing
Worn drive shaft joint - typically these won't produce any vibration unless badly damaged but they can be noisy or 'clonk' for a long time beforehand, turn the steering to full lock and look at the drive-shaft rubber boot there should be no rips or tears in it and the suspension should be clean and dry of any grease. If you reverse at a reasonable speed with the steering on full lock a worn joint will 'click'.
Worn mountings - check the tightness of the engine and gearbox mounts and their condition - this is best done by using a jack to take the weight of the engine off the mounts and seeing if any cracks or splits open up in the rubber.Also check the tightness of the mounts bolts
Broken or defective driveshaft vibration damper - some models feature a rubber mass about halfway along the driveshaft - this functions as a vibration damper so 'tuning out' vibration - the rubber needs to be not cracked and the damper firmly fixed to the shaft and running true - anything other than this and the entire shaft will have to be replaced as they are bonded in place