I love infrared at midday, it's a time when I usually set conventional films aside because IR works so well for me then. My current favourite is Rollei Superpan, which I use with an orange filter, a red filter, with a #87... or no filter at all. I have taken quite a few IR shots within a couple hours of high noon which I thought were quite successful. One particular effect that interests me is under trees at high noon with IR film. The little shafts of light suggest moonlight to me.
Another thing you may find interesting is ultraviolet photography; for that I use a 403 filter, if I remember correctly. Many b&w films have sensitivity down to 400 nm and below; I particularly enjoyed using type 55 (or 665) because I could check my exposures on the spot, but there are plenty of other films which will work well and with a small filter factor. Although skin tones tend to look leathery at those wavelengths (reminiscent of collodion), there is an interesting UV fill effect whereby strong shadows under trees are considerably lighter, and humidity can provide a sort of dreamy, foggy effect.
Another good genre for midday is pinhole, you typically want that extra contrast and light.
I also do a fair amount of outdoor macro (fungus, bugs, you name it) at noon, when the light is strong enough to provide fill under the tree canopy. RE: sunrise and sunset, that genre is way overworked in my opinion. Go bravely photographing at noon and you might well find some new things right under your feet.