The most popular target in April is the Leo triplet, a grouping of three beautiful spirals: M65, M66, and NGC 3628, but there are other, less famous, galaxies this month that are well worth capturing.
M65 and M66 are the best and brightest galaxies this month; while not a bright as M51 or M81, they are nonetheless suitable for begineers. NGC 3628 is larger and fainter, requiring much more exposure time. If your equipment can capture a full degree of sky then you should be able to fit all three galaxies in the same frame.
M95 and M96 form another pair of galaxies in Leo. The brighter of the two, M96, has a beautiful inner core surrounded by very faint, dusty arms. It is also notable because you can see a relatively large edge-on galaxy shining behind one of M96's outer arms. M95, on the other hand, is quite faint for a Messier object. It is a barred spiral and you will need a good deal of exposure time to do it justice.
Another faint galaxy is NGC 3338, a two-armed spiral seen obliquely. But my favorite non-Messier object in Leo is probably NGC 3521, a tightly-wound spiral that reminds me of M63. It is brighter than many Messier galaxies (including M95, M108, and M109) and it is only a bit smaller than M63.
Ursa Major Galaxies
The other major galaxy cluster visible in April is found near the Big Dipper. Its two most well-known galaxies are M108 and M109. M108 is probably one of the faintest Messier objects. M109 is almost as faint, but it is redeemed by its similarity to the Milky Way. Recent research suggests that our galaxy is a barred spiral that looks very much like M109.
The rest of Ursa Major's galaxies are fainter still, and definitely not for beginners. NGC 3953 is a beautiful spiral with tight, well-defined arms. Use as much magnification as you can on it. NGC 3184 and NGC 3938 are both nice (though faint) face-on spirals. But the most interesting object this month is probably NGC 3718, a galaxy of some sort that has been warped and stretched by gravitational forces (probably from the smaller galaxy to its right). Don't be afraid of its magnitude—it is well worth trying to capture.
A few stragglers round out the list of my favorite objects for the month. NGC 3115 is known as "The Spindle," a lenticular galaxy in the constellation Sextans. Lenticulars, which lack the beautiful arms and patterns of spiral galaxies, are not normally on my list, but The Spindle's clean, sharp lines make it an interesting target. NGC 3344 is another face-on spiral, this time in Leo Minor.
We end with two objects much closer to home. NGC 3242 is a planetary nebula in Hydra. It is known as the "Ghost of Jupiter" because it looks like a faint and pale version of the giant planet. Even closer and more impressive is M97, also known as the "Owl Nebula". This planetary nebula is famous because it has two spherical gas regions that look like giant eyes.