I usually prefer Riesling over chardonnay, but there are a handful chardonnays I like. Compared to Riesling, chardonnay is not as aromatic, and how it would tastes depends more on the terroir and the winemaker's techniques. If the soil has a lot of minerals, it have a hint of mineral, and if it was aged in oak, it will taste like oak (toast, vanilla, and coconut). Sometimes you can even taste the yeast which was used to make the wine. Unlike Riesling, Chardonnay is grown just about anywhere in the world, so the wines vary drastically one bottle to bottle. I think getting a good bottle of chardonnay is more important and challenging than other white wines, because there is a huge discrepancy between the good and the bad.
As a general rule for what to expect from chardonnay:
Cool Climate: crisp acid, green apple, citrus, pear
Moderate Climate: medium acid, stone fruit (peach and melon)
Hot: Medium acid, tropical fruit (pineapple, mango, lichee)
Here is the premium list:
Chablis: white burgundy from France. Due to the cool climate, Chablis has green fruit (apple, pear) with citrus aroma (occasionally it might smell like cucumber), highly acidic, bone dry. Since it was grown on limestone, it can also tastes smoky, flinty, minerally. Chablis is the benchmark chardonnay to which everything else is compared to. Premier Cru is the best, but Grand Cru is pretty good too.
Cote de Beaune: Southern part from Cote d'Or. Mearsault and Puligny-Montrachet the best of the region. These wines are fermented in small oak barrels and aged with yeast, so you get a this full bodied wine with a complex succession of flavouring: toast, bread, vanilla, citrus, white stone, tropical fruit, spice. Some people argue that this is the best Chardonnay in the world.
Pouilly-Furisse: This vineyards are grown on a steep slope facing south (for max. sun exposure) in Mâcoonis. They are full bodied with tropical (pineapple, melon) and oak.
New Zealand: Hawkes Bay, Gisborne, Marlborough produces Burgundian style chardonnay. I think these wines have better value than the French wines.
Carneros and Sonoma County in California produces pretty interesting chardonnay. It has intense flavour and very complex.
Casablanca Valley in Chile produces chardonnay with tropical fruit and oak notes.
Mendoza in Argentina produces intense fruit bomb chardonnay
Australia produces a some good chardonnays, but finding it is more challenging. Hunter's Valley, Pathaway, Adelaid Hill, Margaret River produces diverse styles of chardonnays at a reasonable price. Walker's Bay in South African also has a few good chardonnays (if you can find it in Vancouver).