Consider that most tetras are schooling fish that like plenty of their own kind for company, so maybe you should up the numbers of tetras, if you like what you have so far. Neons especially do better in larger groups, behave differently if they have a nice crowd to swim with. Six of would be my minimum, or seven, to have uneven numbers can be be nicer to watch.
And while many of them are quite common, I am rather fond of danios, because they stay in the upper water and are active all the time. Gold zebras are very showy, and Orange Hachets are nice too, smaller. Glowlight Danios are small, and while not very brightly coloured in the body, have a strip of orange down the side that looks like LED lights glowing, hence the name. I like the way they behave and they not expensive, get on well with any fish that is not big enough to eat them.
I like cardinal tetras better than a standard neon, they keep their colour much better as they age than standard neons do. Cory fish are also better in groups of six or seven, with one male to 2 or 3 females, more or less, preferably the same species. You will see them more often and be able to enjoy their antics that way. The albino ones show up nicely, especially on a dark substrate.
If you want bright colours, sword tails are hard to beat, though because they are larger you can't have quite as many as you could of smaller fish. They will cross breed with platies too, so you might not want that. [I'm a fan of the little fishes myself, but I know not everyone likes them so well as I do].
I'm quite fond of Beckford's pencil fish.. the boys have brilliant red fins that just glow when they are displaying. They don't fight, just show off to each other. Girls less colourful, as is often the case. Nice size, peaceful fish.
Red phantom tetra is another colourful fish, very pretty with plants and 'lambchop rasbora' is a lovely little fish in a school. Very bright, active, peaceful fish with a brand new copper penny body colour and a black 'lambchop' mark on the side. Best to have at least six of the tetras and with the pencil fish, two males to four or five females, and plenty of plants, to break up sight lines, so the boys don't have to worry about each other all the time.