I have an idea of using a black hole as a new design of a telescope by placing lenses in orbit around it. Since light bends around a black hole, it should be possible for us to place lenses in a coil around the black hole which would allow for much more room for magnification. This cloud allow us to see much farther than we have ever seen before. However this is just an idea and I would love to hear any criticisms or improvements anyone might have.
Generally, the reason you don't want to stack lenses is because each lens will lose/absorb/reflect some fraction of the light and we don't have a perfect lens. You want as few optical elements as possible. That's why telescopes generally have one large mirror/lens, and a few necessary smaller mirrors for redirecting the light.
Secondly, having a really really large optical instrument is helpful because a larger area collects more light, and a larger aperture is necessary to counter the diffraction effect: see https://en.wikipedia.org/wiki/Airy_disk. There's no way to get around a big cumbersome telescope, and big telescopes have many benefits!
In practice, if we are able to travel light-years to reach a black hole, we have already mastered the art of placing large masses into space. At that stage, we would be able to place huge telescopes in space, and as many of such telescopes as we would like. It would be much cheaper to launch millions of telescopes into the solar system, rather than send one to a black hole. Moreover, we wouldn't want to deal with a light-year-long data transfer time, so having the telescopes be near the center of civilization would be better.
We can use masses as telescopes using gravitational lensing. This does not require us to place lenses near those masses, but rather simply use those masses as the giant wonderful lenses that they are.
Any gravitating body could in principle be used as a lens and as a part of a telescope. See e.g. this discussion about using the Sun as a lens for astronomical observations and possible interstellar communication:
Eshleman, V. R. (1979). Gravitational lens of the sun: its potential for observations and communications over interstellar distances. Science, 205(4411), 1133-1135, doi:10.1126/science.205.4411.1133.
The gravitational field of the sun acts as a spherical lens to magnify the intensity of radiation from a distant source along a semi-infinite focal line. A spacecraft anywhere on that line in principle could observe, eavesdrop, and communicate over interstellar distances, using equipment comparable in size and power with what is now used for interplanetary distances. If one neglects coronal effects, the maximum magnification factor for coherent radiation is inversely proportional to the wavelength, being 100 million at 1 millimeter. The principal difficulties are that the nearest point on the focal half-line is about 550 times the sun-earth distance, separate spacecraft would be needed to work with each stellar system of interest, and the solar corona would severely limit the intensity of coherent radiation while also restricting operations to relatively short wavelengths.
Note the figure of 550 AU appears because the Sun's large size doesn't allow us to use closer focal points. This distance is the main obstacle, since it means that if we wish to observe a single target using the Sun as a gravitational lens telescope we have to send a probe to 550 AU distance (Note that Voyager 1, for example, has traveled about 153 AU in 43+ years). New target for observation would require sending another probe to 550 AU but in a different direction. See e.g. this relatively recent paper for discussion of benefits (such as magnification and amplification/gain for such a telescope) and challenges (besides 550 AU distances) of such solar gravitational telescope (and for references to other works).
On the other hand, a hypothetical civilization that has the ability to travel interstellar distances and has located a black hole without an accretion disk surrounding it could indeed use it as a telescope and surround it with multiple receivers and transmitters (if they also wish to use gravitational lensing for communication) in principle achieving much greater magnifications and gains than “the solar gravitational telescope” by increasing the focal distances. But, on the other hand if such a civilization could easily send multiple probes to light years distances, many other gravitating bodies would suffice for the gravitational lens, not just a black hole.