Flyby near a black hole will gives some totally weird and deformed images of space around it. I can't possibly resume things here, as there are too much things to say. Just run to this web site, which shows many very interesting visual aspects of black holes :
http://casa.colorado.edu/~ajsh/
Without black holes (which will just complicate things a lot), flying at near light speed will also distort the field of view. You'll see about everything around you concentrated in a small area ahead of you, all in blue and possibly ultraviolet, x-rays, etc (Doppler shift). You'll see also all objects behind you concentrated in a small area behind, all in red (or infrared, radio, etc, depending of your velocity).
If there's a large conic collector on the front of your ship, you'll get a huge drag effect. If you move at very high velocity, collisions with the interestellar medium may be, well, catastrophic ! Even without your collector, you will interact with the Cosmic radiation background, which will be very Doppler shifted. Actually, there is a theoretical upper limit on the kinetic energy of moving particles in our universe, because of that field and Compton scatering. I think it's called the Zeldovich effect.
By the way, it is actually false that mass is increasing with velocity. This is another misconception about relativity theory. It's an interesting question directly related to the question "What is mass and what is energy ?". Here's what I may say here :
In relativity, we have
-Relativistic energy of a free particle : E = gamma m c^2,
-Kinetic energy : K = (gamma - 1) m c^2
-Proper mass energy (or rest energy) : E0 = m c^2.
Here, gamma is the relativistic factor.
We can also write E = E0 + K.
Mass is actually an intrinsic property of matter and is defined by the PROPER mass of the object, as measured by a comoving observer. It is simply m and is a constant, whatever the velocity. In most books, we write m0. Sometimes, we can write also
m = gamma m0,
but this is only a matter of convention and is not physically mesurable. I hate that notation, because it is the source of the misconception. Here, I use only m == m0.
It is true that energy is equal to mass, but NOT the kinetic energy part ! It is the "proper mass energy" E0 which is equal to mass. We must be carrefull to say what kind of energy we are talking about.
"Well! I've often seen a cat without a grin", thought Alice; "but a grin without a cat! It's the most curious thing I ever saw in all my life!"
