Hi Mark,
There is one way to see dimmer objects with the Moon rising - view in the direction furthest from the Moon. These will be the lease affected for longest. If you have a 10" scope, you will have no problem viewing mag 8 objects. The Moon's phase this weekend is not it's worst, so working with it isn't mission impossible.
Galaxy wise, there is plenty on offer. The one's I'm listing won't be a problem for you 10". Only one, the last one noted, could be just too late to view by the time the Moon rises.
* M65, M66 and NGC 3628 in Leo. These are a trio of galaxies all very close to each other, and all visible in the one field of view (low power). These are all at different angles to us, one is quite round, another ovoid, and the third, and faintest, is nearly edge on.
* M95, M96 & M105 in Leo. Another fine trio all visible in the same FOV.
All six of these galaxies are in the mag 9 range, and all EASISLY canon fodder for your 10". In fact, I saw the M65 trio from my home in Sydney two weeks ago through a 10". You will have no problem if you are anywhere in a relatively dark site!
* M87 in Virgo. You will need to have a decent view to the north to spot this Monster. If your northern horizon is clear, this colossus of an elliptical galaxy is also easy, even in small scopes. It will appear as a globular cluster that just won't resolve into its component stars. I managed this sucker from home once too, looking through the light dome of Sydney's CBD. Bright bugger for a galaxy too at mag 8.6.
* M104 in Virgo. Now we're talking sexy!
This bugger can prove illusive to find at first. But once pinned, it takes magnification really, really well. For it being edge on to us, the dust lane shows a lot of detail. Bright too at mag 8.3.
* NGC 5128 in Centaurus. At mag 7 it is one of the brighter galaxies, but it is spread over a relatively large area so it can appear faint. The "Hamburger" galaxy is very close to Omega Centauri too. I've seen it from a dark site using just a 6X30 finder, so you won't have trouble seeing it in your 10" scope.
* M83 in Hydra. It is one of the few spiral galaxies that we can see its spiral structure. You might have a chance to see it two of its arms with patience and not being afraid to up the magnification with it in your 10", but it will test you big time. The main problem with M83 this weekend is the Moon will be hard on its heels. Next weekend will it will be a better proposition.
Like a few more?
Mental.