With a dozen obelisks scattered around Rome - not counting a few modern examples - it can happen that you just stumble across one. That's how I found the Celimontana Obelisk.
We had been visiting the delightful Casa Romane del Celio site and decided to walk over to the Baths of Caracalla. When the gates of a pleasant garden appeared along my proposed route it was easy enough to nip on in. The gate we entered was off of the Via di S. Paolo della Croce, and brought us into the gardens associated with the Villa Celimontana. This is on the Caelian Hill, perhaps the least known of The Seven Hills.
The villa is much renovated and now serves as the headquarters of the Italian Geographic Society. The associated gardens are a public space, and are a delicious quiet retreat from the nearby Tourist Chaos of central Rome. And the best part was that we rounded a corner and saw this:
If you think this obelisk looks to be a bit of a hodge podge, you are correct.
The history of the obelisk follows some familiar routes. It erected by Ramses II, and was one of a pair that stood in front of the Temple of Ra in Heliopolis near modern day Cairo. They were transported to Rome in Imperial times and were part of the Iseum, the Temple of Isis, that stood near the Pantheon. This site was the source of numerous extant obelisks.
At some point this one was moved to the Church of Santa Maria in Aracoeli on the Capitoline Hill. It was in any event there in the 14th Century. It appears to have fallen down and/or been moved elsewhere.
Fast forward to circa 1582 when the Senators of Rome gave the Obelisk as a present to Duke Mattei to help decorate the grounds of his new villa on the Caelian Hill. As a present it was a bit of a Dog's Breakfast, composing parts of several other unidentified obelisks mated to the upper section from Heliopolis.
The villa and grounds were not kept up all that well, and the obelisk again fell over. It's not all that surprising, the patched up bits of several structures must have been rather unstable.
A Spanish stateman named Manuel de Godoy lived in the manor in the early 19th century and undertook to restore the obelisk and to have it moved to a better location. In the process of reseating the obelisk a workman had his arm accidently pinned under the base and amputated. Because they were not about to lift the obelisk up again it is still in there.