A 60 mm refractor is a lttle on the small size fo looking at most galaxies, as the galaxies subtend a few arcsecond to arcminutes of the sky and are quite faint for most scopes below 100mm, there are a few bright galaxies that can be seen ,such as the LMC,SMC Ngc 253 M31 Ngc 3128(Cent A)
ect.but they will quite faint, all he above can also be seen in your bino's but again quite faint.
I would sugest that you may concentrate on some of the brighter DSO's that are coming up in the Milky Way centre in the next few months to give you a better understanding of locating, size, and magnitude of these object and then if you get a bigger scope you will know what to look for and have a bit more knowledge to persue your hobbie.
In the meantime get a good Planesphere and some star charts, or a computer program and you will be off and running.astroron
