Sometimes I'll be seated at a 4 person table when I visit a restaurant with one other person. When on a first romantic date with someone, what is the etiquette as to whether I should sit beside them or across from them?
Generally, at least in Western culture, you'll sit across from your date. You can verify this by checking out a wide array of romantic movies. I can't recall any where the couple sat side by side leaving the two seats opposite them empty. It makes sense this way because on a first date you are probably watching your date's reactions pretty closely to see how things are going.
The other data point I'd add is that when I show up to a restaurant with my wife and am seated at a four person table, the wait staff always seats us opposite each. They don't ask, they just pull away the two extra place settings.
I've spent most of my life in the USA but have traveled some in western Europe so this isn't strictly a USA custom.
In the United States, it's typically expected that you sit facing your date when it's just you two; especially on the first one.
The reason for this decision is so you can converse face-to-face, making it more personal. You'll be able to view their expressions and really take in all the good stuff like body language. This is really important on the first date specifically because it's an imperative time to start knowing if this is a person you'd like to see for the foreseeable future.
Body language and facial expression is so important to human interaction; sitting aside them will only make it difficult to observe this. A table with four seats might seem kinda awkward, but the technique still applies because you want that interaction.
Might be personal preferrence, but something to consider: it depends on the table layout. On many occasions I got sit on a round dinner table. In such situations, if you sit on the chair next to your dates one, you sit in like a 90 degree angle to each other. That setup allows for a regular conversation, where you can look into each others face, but also gives you the chance to be a little closer to your date if things go well. This advide is especially important (to me) when going out and having some drinks for example, instead of dinner.
Otherwise I totally agree with the answers mentioned before.