The brands I have listed here, except for one, are of ukuleles I either own, have bought as gifts or have played, so I'm not just regurgitating company PR!!
My first ukulele, the obscure brand of which I can't quite recall, caused a lot of frustration over the few months I played it as it was a seriously below par (but not especially cheap) instrument. To prevent anyone else from suffering this frustration, I reduced it to kindling.
aNueNue means rainbow in Hawaiian. This company proclaims itself to be multi-national with operatives in Hawaii, Canada, Taiwan and Japan. The ukuleles are quality instruments and like all ukes, have their own sound due to the wood chosen, the shape and the stringing (aNueNues seem to have tighter strings than some others). Their range is from entry level to professional. I play a Lani III E tenor and it is my friend.
Cole Clark make high quality guitars in Australia and have now branched into equally high end ukuleles as well. They have a small but very well designed range, all of which have pickups for amplification.
Kala is one of the world's best known brands, based in Hawaii and begun by a bass player....which may explain why they also make the highly successful U-bass or bass ukulele. They have 120 different models including a pocket ukulele and a travel ukulele. They also manufacture Makala, their entry level brand.
Kamaka...what more need I say? The company's founder began making ukuleles at his home in Hawaii in 1916, it's the brand Jake Shimabukuro plays, and they are now available at Jack's Music in New Lambton, NSW Australia!! The day they arrived I was lucky enough to have a play of one. As you can imagine, they are exquisite - in look and sound and have perfect harmonics no matter how far you go up the neck. Jack's is one of only three Australian Kamaka dealers, the other two are in Cairns (Q) and Perth (WA).
Lag ukuleles are part of the Lag guitar family, started by a French luthier and guitarist. They are very attractive and not the cheapest instruments, but their good looks and playablility sell themselves!
Lanikai make quality ukuleles for players and performers, a step up from entry level and beyond. They are reliably good and generally well priced.
Leho is a relatively new brand of ukulele (it means 'seashell' in Hawaiian) but the man behind it has years of production experience with a large well-known brand. These ones are very attractive with an unusual arched back and are good value for money. Rumour has it they are bringing out a bass ukulele!
Mahalo - meaning 'thanks' in Hawaiian, is a major brand, has origins in Japan, and is manufactured in China. The brightly coloured entry level ukuleles in their range are often the first ones new players try out or purchase and the company has a commitment to quality at a good price, for all their ukuleles.
Maton is one of Australia's premier brands of guitar and they have moved back into ukulele production for the first time since the 1960s. Maton were very supportive sponsors of the inaugural Newkulele Festival in Newcastle and have a well-earned reputation for quality, craftsman built intruments, often including Australian woods.
Scott Wise is a master luthier from Margaret River in Western Australia who makes a range of instruments but the ukulele is a particular passion. I've seen one of his daughters, Lucy, an established singer and songwriter, playing one of his ukuleles while performing and it looks and sounds phenomenal.