Over the last month I've been using a Canon IS 12x36 for both birdwatching in daylight and astronomy, and while the performance during day hours leaves something to be desired in terms of sharpness and (especially) chromatic aberration, the night performance is simply stellar. I'm talking about hand held use here, and they're simply magic. You press the button and suddenly you're floating effortlessly in space, gliding from one constellation to another, double stars are split so easily, and clusters show distinct stars. I like the fact that they have a fully usable 5º FOV (while +6 º is the norm among 10x50 binoculars, is not that unusual to find very capable 10x50 models with a mere 5º FOV, which for a 12x I find more than acceptable). During the night, comfortably reclined on a chair with the Canon IS 12x36, the IS really show their strength. They're well within your budget. Yes, IS takes some getting used to and has many quirks and downsides, but you simply see more (more detail, more stable).
If you are looking into handheld astronomy binoculars, I can recommend Roger Vine's website scopeviews.co.uk, where he makes reviews of binoculars with astronomy in mind. Anything from Zeiss (more than 10 different models), Leica, Swarovski (again, more than 10 models, several "big eyes"), Meopta, Fujinon, etc.
One very interesting thing is that, when reviewing any model he always makes a direct comparison with other similar (and well-known) one, so you have a reference. The Canon IS 12x36 are one of his current favourites. You can check what he has to say about them both in the in-depth review and also in his "Best Buys" section:
Best Buy Astronomy Binoculars
Canon 12x36 ISIII
You want high-power binoculars for finding and enjoying brighter DSOs and for quick looks at Luna or keeping track of Jupiter’s Galilean moons, but you don’t want to pay thousands. What do you buy? Well, I can tell you what I’ve bought - Canon’s 12x36 IS IIIs (not the older ISIIs, yes it makes a difference). Many cheaper high power binos are a bit compromised optically or mechanically, which usually means bad for astronomy. But these Canons have truly excellent optics, a smooth accurate focuser, decent eye relief for glasses wearers and a very light weight of about 700g with batteries.
All those things alone would make them good value, but the killer feature is of course image stabilisation. In this latest version (IS III) it just works ... and then some. Not only does this give you amazingly detailed views of the Moon, but wonderful deep sky performance too, despite the modest aperture. Even more surprisingly, planets too – I had great views of the recent Jupiter/Saturn conjunction with both planets clearly and distinctly resolved, Saturn with its handle-shaped rings.
They may be just 36mm aperture, but the stabilisation allows them to outperform good 12x50s for astronomy in many ways. The main downside is too much false colour for some terrestrial uses (birds on the wing, or nature viewing over bright water or snow), but that’s not an issue for astronomy at this magnification.
Yes, I know they’re a piece of consumer electronics, but if you want outstanding astronomy performance for a sensible price, these are my top pick.