I'd have thought you'd be on a compound if you're military. This is good because it means you'll have a shared pool - always a bonus. All the military people I know live out Seeb way - it's fine.
How old are your children? The school you send them to depends very heavily on where you live. There are 4 main choices, but also others which are employer specific. I have an inkling of an idea that there is a school for Military children out near the airport... but I might be completely wrong about that. If you do live towards Seeb you'll probably choose Royal Flight School.
The 4 main schools are...
The British School - fine, British curriculum
ABA - good school, IB syllabus
TAISM - American syllabus, fab facilities, more expensive than the others.
Royal Flight - Seeb end of town, British curriculum, nice school.
There are also a lot of nurseries to choose from if your children are younger, and some of them go up to age 6 or so. TLC is growing from a nursery into a school and currently goes up to Year 4 I think.
Schools tend to be oversubscribed and generally have waiting lists. Best to make contact sooner rather than later. All have websites.
Muscat is a friendly place, nice for kids, fairly sleepy. It's great if you like outdoorsy stuff. Camping, exploring etc. Beaches are gorgeous. You can get most things you need but the shopping isn't fabulous. Dubai is only down the road if you need to do some proper shopping. There's an Opera House for a bit of culture, a smallish cinema, a bowling alley, a new ice rink, a couple of malls, 4 or 5 huge supermarkets. Alcohol is regulated but not banned. A couple of restaurants and all the big hotels have licences, and you can get a licence to drink in your home. Groceries are fairly expensive - possibly on a par with UK? Petrol / running a car is hilariously cheap.
The weather is horrendously hot for about a 3rd of the year. Ramadan is pretty grim for expats as everything shuts and you can't eat or drink in public - most expats tend to clear out for most if not all of Ramadan. The rest of the year is nice weather.
If you're military then you'll have housing provided, you'll get to know your neighbours - ready made social life with the other military wives. Not much else to tell you tbh.
Is this your first overseas posting?