Substitute for alcohol syrups in cake?

Realistically, vanilla extract is 35% alcohol, which is 70 proof. Flavorants or not, it wouldn't be any less intoxicating than rum if you drank it straight. That being said, I don't think its inappropriate putting a little alcohol in a child's cake, keeping in mind that children don't often care for the flavor or rum or brandy. I also happen to know that people who self-identify as alcoholics, don't often appreciate the flavor of alcohol either. The small quantity of alcohol, however isn't going to affect a child's physiology any more than sugar or caffeine.

Now, since I don't want to surprise guests with the zing of rum when they're not expecting it (I always warn people). I often like to use a solution of orange blossom water and simple syrup for cakes it will benefit like chocolate or carrot. I also like to use rose water syrups, dark honey, strained jams (thinned a bit), espresso, brown sugar simple syrups, maple syrup (thinned), a thin caramel, syrups infused with herbs, etc.

in addition to Cynthia's vanilla idea, here are some useful substitutes:
for rum, Molasses mixed w/pineapple juice & almond or rum extract
for brandy, grape juice (white or low sugar is better than sweet dark purple)
for flavored liqueur, a fruit juice or puree, or concentrate (extract, oil etc)
for ale or lager, use broth or flattened ginger ale.

P.S. I know that vanilla extract is alcohol-based, but not strictly alcohol, as in traditional rum or brandy.

You don't need the alcohol, but the moisture will be useful. Depending on the fundamental cake flavor so, you could make similar syrups flavored with orange juice, lemon juice, coffee, or juiced berries, or a simple unflavored sugar syrup.