The Moon will move appreciably from one day to the next, but Jupiter will be in pretty much the same spot, at the same time, for a while to come.
(It will get to the same position roughly 2 mins earlier each day/night)
If you get the chance, point some binoculars at Jupiter - as little as 10x will show the 4 main moons spread out in a line either side of the planet's disk.
It can be fascinating to watch their nightly 'dance' around the planet as they shift position from one night to the next.
Sometimes they will be all at the same side. like this...
• • • • O
Or maybe two each side...
• • O • •
Or one and three
• O • • •
At times, less than 4 may be visible, if one or more is directly in front, or brhind the planet.
A bit more magnification, from a birding spotter-scope if you don't have an astronomy telescope...
You should be able to see cloud banding on the surface, or even shadows of Moons passing across the face of the planet.
Here's a sketch I did last week, using a little over 200x magnification.
The black spot on the planet's surface is the shadow of the moon just to the right of the planet (Ganymede) - the 'half-blob' on the far right of the lower main band, is the Great Red Spot disappearing around the planet's limb.
The letters along the top identify the moons Io, Ganymede, Europa