You can try TAKA Jewellery in Causeway Bay (East point road, between G2000 and Giordano, close to SOGO)
See the website : Taka Jewellery
I bought a ring there recently...I think it was all right (nice and not too expensive).
Up to you and congratulations !
We were happy with the service and pricing at Gaily Jewellery in Queen's Road Central (near the big Sasa sign).
I got married in Hong Kong last year and the ring issue was a tough one.
In causeway bay, if you walk from Sogo towards Wanchai, you will find plenty of smal jewelery. The best thing is to enter some of them and do the benchmark. You can bargain, i got mine for quite cheap in the end and the quality is good.
And then, it all depend on the style of ring you want. I wanted something very simple but it seemed simple was impossible to find in Hong Kong except at Tiffany's....
Not sure what you mean by not too expensive but the big names here: Chow San San, Chow Tai Fook, TSL, 3D Gold....will set you anywhere between 1K to 5K which IMHO is pretty correct.
More international brand (Tiffany & Co, Cartier)....will start from around 8/10K minimum
I believe Hullexile means the jewellery store called ??, which is directly opposite the Wanchai MTR station on Johnston Rd, by the corner of the zebra crossing.