Can I take tylenol (acetaminophen) with acyclovir, as I understand ibuprofen is probably not a good choice considering the impact on my kidneys by both drugs?

Yes, but... Oral Acyclovir does not hurt the kidneys. That only happens with intravenous acyclovir.
Probably OK. Unless you have problems with poor kidney function and if taken as directed there should be no problem. Also, tylenol, (acetaminophen) which is Acetaminophen does not have much of an adverse effect on the kidney. It is the liver one should be concerned about with this drug.
Ask your oncologist. Tylenol (acetaminophen) is a benign medicine when taken properly. More than the recommended dose can be very toxic to your liver. Some chemotherapy drugs including Acyclovir can affect the liver so ask your oncologist what to do. Ibuprofen may sometimes be ok and more helpful but clear it with your doctor first.