What is a quality, inexpensive lens, with good image quality?

[RobertTheFat]

For what camera??

[rivernuzzo]

Rebel t6i

[ScottyP]

You have the T6i. I assume it came with 1 or 2 "kit lenses"?

What sort of shooting do you want the improved lens to do?  What focal length are you looking for?  Walk-around lens?  Telephoto sports lens?

if you have the kit lenses, they are zoom lenses and they cover the most commonly used focal lengths.  To see a real improvement in image quality you are looking at larger aperture "faster" lenses and/or at sharper ones. 

The oft-suggested Canon 17-55 f/2.8 has a larger aperture and is a bit sharper than the kit lenses. It is a good choice but at $800 new or $550 used.  

Non-zooming fixed focal length "prime" lenses are another way to go. Typically a prime is sharper, larger aperture, lighter and also cheaper than a zoom lens of comparable quality.  Possibilities would include a 50mm f1.4 or a 40mm f/2.8 or even an EF-s 60mm f/2.8 MACRO lens.  The latter would give you the ability to shoot macro shots of tiny bugs and things.  

[ebiggs1]

"Rebel t6i"

However, this was you second reply.  The Rebel T6i is a fantastic camera and is capable of outstanding work. It really deserves a lens like the one mentioned above. The Canon EF-S 17-55mm f/2.8 IS USM Lens.  This lens has many features that are worlds apart from the standard kit lens(s) you may already have.  It does not meet your 'inexpensive' goal.

Main advantages are the f2,8 aperture.  Add to the fact it is a constant aperture, big difference here! Generally better IQ across the board. Faster AF and better build. Besides it is an awesome looking lens! That counts for something. Right? It may well be the best ef-s zoom lens Canon offers.

Disclaimer, I do not own the Canon EF-S 17-55mm f/2.8 IS USM Lens but I have used a couple of my friends lenses.  I have done post for them so I believe I speak from some experience.

[Waddizzle]

"What is a quality, inexpensive lens, with good image quality?"

Almost any Canon lens that has a model number that ends with "STM". 

You're asking for a specific answer, but without providing specific requirement details.  Without knowing your interests, specifically focal lengths, there is no specific answer to your question.

[kvbarkley]

While all of these are relative, the lens that comes closest to your requirements is the EF 50MM.

[TTMartin]

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@kvbarkley wrote:

While all of these are relative, the lens that comes closest to your requirements is the EF 50MM.

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I would go further to say the EF 50mm f/1.8 STM. 

The older EF 50mm f/1.8 II has a lower build quality and an inferior focus motor.

[ebiggs1]

"What is a quality, inexpensive lens, with good image quality?"

Without knowing any additional info I have to agree with my compadres.  Often, I don't do and I rarely recommend the 50mm f1.8 lens, any version.  The latest one, if you do get one (the newest version), will offer the best IQ for the buck. It satisfies all three points of your question.