What are some tips for finding non-generic hashtags on Instagram?

I'd recommend defining what type of art you are seeking to find on Instagram. For example, optical art is a specific type of art. After some searching on Instagram, I was able to find #opart, which focuses on this particular type of artwork.

To become more noticed on Instagram, I'd recommend finding a niche. Instead of creating an Instagram account about art, a better strategy would be to create an account about a specific type of art such as optical illusion artwork.

The more specific you are about your niche, the better you are positioned to grow on the Instagram platform.

Try typing one of your 'generic' hashtags into the app’s search bar, and then select “tags” from the dropdown menu. You’ll then be able to see all of the top hashtags that are closely related to your hashtag, revealing additional ways to reach, monitor, and engage with your community.

Beyond researching by way of competitors and industry leaders for hashtags, you can find out what hashtags your audience is using and see which ones fit the content that you’re publishing. Your hashtags should be relevant and contain keywords that users are actually searching for.

Social Media is not as easy as some people make it seem. It is also not as hard as it appears, the trick to it all is - specially in getting others to truly like you - is to find a niche and speak only to that interest.
With that in mind you could narrow down hashtags to cater situations. For example, you used the word #art (Besides being a global strategist I am also an artist and my first love was painting) I can tell you that the hashtag art will generate a broad exposure, specially on Instagram but then you need to narrow it down to situation such as who's posting/who you want to target? The person? the building? the buyer? who? You can narrow down #art to #artist or #artists then to #artgallery then #abstract or #popart then tools used such as #stencil or #photoshop and then possibly add to your hashtags some muse tags that might provide inspiration for artist such as #scenery #galaxy #landscape #murals #wearableart etc

You can also type these narrowed tags one you have identified them and see the "related:" suggestions Instagram gives you.

My name is Humberto, I'm the founder of www.Unthink.me, a digital marketing agency that brings big business tools and experts to small growing companies with little budgets. Best of luck in your efforts!