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Perhaps the brightness of the moon will make it hard to see much more than you've described at the moment. I'm fairly new to this obsession myself and do alright in finding nebulae, galaxies, clusters etc. but I don't look for much other than moon, planets and globulars while the moon is about. I hang out for the dark skies. If you point some binoculars around Sagittarius, find some fuzzy bits and then point your scope at them you'll definitely see some interesting things. But perhaps wait til after the full moon when you will have a few hours of dark before the moon comes up to explore.
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