Cairo Metro Line 1 has a Nozha station serving the eastern edge of Heliopolis, making the suburb accessible from central Cairo in around 30 minutes from Tahrir Square. Taxis and Uber are easy from anywhere in the city and relatively cheap by international standards.
The historic tram (Line 2) still runs through the suburb, connecting Heliopolis to the Abbaseya area to the southwest. It is slow and irregularly maintained, but it is also the last surviving tram line in Cairo and atmospheric in its own right.
From Cairo International Airport: Heliopolis is only about 10 minutes by taxi — closer to the airport than to central Cairo. This makes it an excellent option for a layover visit. If you have three or four hours between flights, you can comfortably walk the main streets, visit the Baron Palace, and have lunch before heading back.