His side has won the first battle and drawn a home venue for the fixture against Auckland side Bay Olympic on either August 14 or August 15.
The other semifinal will be played in Wellington, with Miramar Rangers at home to 2008 champion East Coasts Bays.
Fleming, who has previously raised concerns about the legitimacy of the draw, said a home game was a big advantage.
"We're very pleased that we are playing at home," Fleming said.
"We went away in the last round so it is just the luck of the draw. You need a bit of luck and we're grateful to have some.
"You can get out of your comfort zone a bit [playing away]. You have to get a flight and if things don't run smoothly you can get behind.
"I've been on many a trip to Auckland where you have to get changed on the bus on the way to the game. Those things are unforgiving and take a toll on the guys."
Caversham will not have any of those sorts of distractions.
Bay Olympic, on the other hand, faces the daunting trip south.
Bay Olympic coach Shane Knowles, who was present for the live draw made on Radio Sport, reportedly winced when he realised his side would have to travel to Dunedin.
"The boys are always keen on away trips but ... it will be tough," Knowles told Radio Sport.
"You've got to beat good teams to win the cup. Caversham are top of their competition down south so it will be a tough game."
Fleming could not be drawn on whether Caversham had a favourable semifinal opponent or not, but said Bay Olympic played in a very competitive league, were a wealthy club and "over the last few years have put a really good team together".
"I'll be trying for the next three weeks to get the best out of my team so we're positive and can go in and enjoy the occasion."
Fleming questioned the genuineness of the quarterfinal draw which paired all four Auckland teams together, the two Wellington teams and the two South Island teams.
