I look to spend three nights in Murten and us it as a base to visit Bern and the Swis Jura. Or, should I just stay in Bern as a base? Also, waht is the driving time from Murten to Basel?
You can google estimates drive times
e.g.
https://www.google.com/maps/dir/Murten,+Switzerland/Basel,+Switzerland/@47.2505046,6.9178033,9z/am=t/data=!3m1!4b1!4m14!4m13!1m5!1m1!1s0x478e12fc38054091:0x99458eceba34cd69!2m2!1d7.120184!2d46.9292211!1m5!1m1!1s0x479049c72769304f:0x361ceb70f36d8a90!2m2!1d7.5885761!2d47.5595986!3e0
If you are travelling by car a small town like Murten is a better place to stay than a city like Bern. Be sure to ask if your hotel has parking.
According to https://www.viamichelin.com/ Murten to Basel is 01h30 (124 km) by Autobahn, which sounds about right if you don't hit any traffic jams and don't stop.
But, I would suggest the more scenic route via the Jura: Biel, Moutier, Delémont, which viamichelin says is 02h23 (125 km)