If you're looking for a very elegant accent chair, then this Oliver fabric chair or this Tulip leather chair from West Elm would be a very good option. These West Elm upholstered chairs feature very smooth lines and round shapes which would really soften up a space and make it feel rather sophisticated and elegant, without going overboard. These chairs definitely have a modern look to them, but they don't feel like they are contemporary all the way, instead it feels like a good in between of new and old where good materials and clean lines are in focus.
At West Elm you can overall find a really nice selection of living room furniture, as well as pieces for the dining room, bedroom etc... All of these West Elm furniture are actually quite affordable which is rather surprising since this type of nice design is often pretty expensive. Within their selection you can find quite a few options to choose between, so it shouldn't be too difficult to find something which would work well with your budget as well as sense of style.
Tulip Leather Chair
"The curvaceous, contemporary silhouette makes this a sumptuous haven for reading and relaxing. Luxurious leather upholstery. Comfortably padded, removable seat cushion. Durable wood base. Wood legs with radius detail. Fully assembled"
"A comfortable embrace of a chair—with a rounded shape, feminine lines and scaled-down proportions that are perfect for smaller spaces. Chunky cotton basketweave upholstery over comfortable polyurethane foam padding. Solid wood chocolate-stained legs. Rounded silhouette has feminine lines and a smaller profile."
These furniture are from westelm.com