While you are visiting Lake Como you should set aside a day (at least) to visit Lugano, Switzerland. From Menaggio it is less than a hour away by car; usually much less. Take your passport with you just in case you are asked for it at the frontier. I have never been asked to show any kind of ID, but it is always best to be prepared. Just slow the car down as you pass the various border crossing signs.
Once in Lugano, I would suggest parking in the Cassarate area (as you arrive in the bay of Lugano) and walking from there. Driving around the mostly one-way system of Lugano you will miss the real highlights. However, from Cassarate you can walk along a leafy avenue, and cross a small bridge over the Cassarate River, to the Parco Civico. In Parco Civico they often have cultural activities, especially at the weekend, and the waterfront walk is delightful, in any season. There is a lovely new children’s area there too.
The Parco Civico ends near the Casino Lugano but the promenade continues all around the bay. However, you may be tempted to cross the street to the Piazza Alessandro Manzonito where the fountain, carousel (sometimes), shops, cafes and restaurants will attract you to spend some time. Beyond the square, you will find all kinds of streets and alleyways to explore. Little piazzas seem to pop up out of nowhere and enchant you as you discover Lugano. There is an embarrassment of designer shops in Lugano and an abundance of specialty stores too. And don’t forget to visit the famous department store ‘Manor’; their basement cafe and food department is worth a visit by itself.
When you have explored as much as you can manage for one day, head back to your car. Just a tip about parking in a new (to you) place: take a few photos on your phone so that you can back-track and don’t have to spend a hour searching for the car (especially if it is a hire car and you are not too familiar with it!).
Set aside at least half an hour for a break in your journey back to Lake Como. Once back in Italy the road will lead you round to Porlezza at the tip of Lake Lugano. There is only one road, so no directions required. It is well worth parking the car and relaxing at one of the cafes or bars on the waterfront, and enjoying the emerald green lake before you leave it behind (for now at least!). The afternoon sun is splendid in this sheltered enclave of the lake and you can sit back and really feel that life is good!
By the way, Switzerland still has its own currency, Swiss Francs. However, most places will accept Euros, but provide your change in local currency.
Another tip: It is possible to take the local bus C12 from Menaggio to Lugano and back. It takes a couple of hours but only costs a couple of Euros. Ask locally for the bus schedule.