What do you mean by "not too expensive"? That somewhat vague, isn't it? To me, it means under $75 a bottle.
In that class, Tesseron Lot 90 XO has most of the qualities you're looking for. I think I paid around $53 or $57 a bottle, somewhere in that range. It's one of the few spirits I prefer to buy by the case. It has the almond and stone fruit notes, is nicely oaked, but it lacks any caramel flavor. It's one of my favorite for the snifter due to the excellent quality at a reasonable price. In the Tesseron lineup, Lot 76 and especially Lot 53 are easily more satisfying, but neither of those have the almond and stone fruit characters, and they are considerably more expensive too.
A cognac that does have the caramel notes, but does not have the other characteristics you are looking for is Chalfonte VSOP. It's also underpriced, in my opinion, at around $26 or $29 a bottle. This is not the best cognac in the snifter, but it is excellent as a mixer, especially in a sidecar.