To be in Rome is to be right at the centre of Italy and its culture. To find yourself bored in Rome is virtually impossible and, as Goethe wrote in "Italian Journey", "To take in even a small part of everything there is to see here would take a lifetime or, rather, the lifetime of many human beings learning from each other in turn". Rome is a large city so the direction you should choose depends very much on your mood for the day.
To immerse yourself in Roman history a short taxi journey will take you to the Forum and the surrounding Roman remains including the Colosseum, and the Capitoline Museums. A walk on the Palatine Hill is one of the most enjoyable ways of retracing the Roman past and another relaxing place to leave behind the noise of the city is to head for Trastevere where a different side of Rome can be experienced in its quiet atmospheric streets and squares or by walking in the parks and gardens that fringe the hills above this western side of the city.
If your mood leans towards art and architecture later than the Roman legacy, be sure to visit the splendid Piazza Navona and while in that part of town see the atmospheric Campo dei Fiori. Over the river from here is the splendid Castel Sant'Angelo and the Vatican with all the majestic splendour of St Peters'and the Sistine Chapel. Nearer the hotel is the famous Trevi Fountain and all over Rome are hundreds of fine churches filled with treasures from the past. If you want to walk somewhere else close to the Regina head up the Via Veneto into the Borghese gardens, on to the Pincio and the fine Belvedere above the Piazza del Popolo where the Via Flaminia once entered the city. From here it is a short walk past the Villa Medici to the famous Spanish Steps and into the centre of the shopping area around Via Condotti. Bored you will never be.