Drinking plain water is the most common way it's consumed across Tamriel, but you are indeed correct that many enjoy flavouring theirs for a bit of perk during the day, or to wind down in the evening.
Fresh flower petals, especially jasmine and rose, are used to add some delightful aroma to both still and sparkling spring water in Summerset. The gentle floral fragrance can take a bit of getting used to, but it's quite relaxing (and delicious with gin)!
Argonians value their potable water sources, and very rarely add anything to it. However, some enjoy an infusion of cucumber slices in cold water, which is the perfect drink to moisten the scales on a hot day!
Exceptions to this trend are the Bosmer, who prefer their water pure. Not to mention that meat-related water infusions are generally called a broth...
Fresh fruit, especially raspberries, apples, and lemons, are High Rock's choice when it comes to flavoured water. Sometimes the fruits are muddled, making it more of a diluted juice than water.
Comberries and fresh marshmerrow sticks are a cup of water's best friend in Morrowind, especially on a hot day. Comberries impart a slightly bitter flavour, almost like tonic water, while marshmerrow imparts a lightly sweet, candy-like aroma. Both taste great still or sparkling.
Herbs and aromatic plants are the most common infusions in Cyrodiil, such as rosemary, mint, and lemon verbena. Jars of water are infused overnight with fresh herbs (lightly crushed to release the aroma), and chilled or served with ice. They can sometimes be a bit pungent, but still enjoyable.
Moon sugar aside, the Khajiit love flavouring their water with fresh vanilla beans and rose petals. This sweetly scented beverage is great for any time of day, and is wonderful both warm and chilled.
Juniper berries, jazbay grapes, and lavender are a Nord's choice for flavoured water, though we'd honestly rather just have mead instead. These plants are relatively easily obtained across Skyrim, and impart relaxing aromas that are best served as a nightcap.
The Orsimer of Wrothgar flavour their water with wrathberries, which are both peppery and bitter. The end result is a warming drink that burns like whiskey going down, but doesn't contain a drop of alcohol. Perfect if you've caught the chills, especially with some ginger.
Like the Bretons, coastal Redguards love using fruit to flavour their water, like fresh coconut, pineapple, and mango. However, Alik'r Redguards prefer mixing cactus slices or aloe vera into their water, which gives it a refreshing, sour twist.