Plenty to do and the car will give you a lot of freedom.
Orta San Giulio is about 15 mins' drive from where you are staying. The town is pedestrian and you'll need to park on the outskirts and walk down. Take a stroll around the cobbled streets, go to the island and visit the sacro monte. There's also a two star michelin restaurant in the villa crespi hotel, if you're interested.
Omegna itself is a nice little town with a lovely lakefront promenade, Thursday is market day, selling everything from chicken and fresh cheese to shoes and handbags - well worth a visit and you might see some of the old ladies in local costume (they come from the surrounding valleys and villages for market day). If you're interested in design, this is the home of Alessi and they have a factory shop and showroom here.
Drive up to Mottarone for a view if the lakes and they also have a theme park called alpyland with a rollercoaster that hugs the side of the mountain. Alternatively you can drive to Stresa and get the cable car up.
Staying on the Orta lake, you can drive around to the opposite side and visit Pella with the Modonna del Sasso.
For the best view of the lake, drive up to Quarna Sopra (above Omegna) right to the end of the road at Belvedere, unparalleled views from here imo. There's a lovely restaurant on the way up, the Locanda Posta in Quarna Sotto.
Then there's lake Maggiore, stresa, the islands, cannobbio, the gardens at villa taranto and alpino, the eremo di santa caterina on the opposite side, arona. You can also take the ferry up the lake into switzerland and the train over the mountains back (maggiore express)
Another option is to up to the mountains and valleys, val strona, val d'ossola, val sesia.
So, a lot to keep you busy!
Those are some really wonder suggestions! Thank you!
Two weeks is enough time to taste the whole region!
Then you could drive south to the hills between Langhe and Monferrato, with the castles, the great food and the vineyards at the begin of their autumnal colors.
You could go on THE LAKE MAGGIORE EXPRESS. A Narrow Gauge train which can be got from Stressa onto to Domodossola whee you board the Swiss train to Locarno, its a scenic route in a panoramic train. You get a Boat trip on the return to Stresa. Good value for a whole day trip. I think its 40.00 euro and you can pay an extra 10-12 Euro and you get another day pass the following day on Lake Maggiore. Interestingly for some the Swiss train company go by the unfortunately named F.A.R.T. so its yes you have guessed, the FARTing train.
Would it be better to do the Maggiore Express on a Sunday or a Monday/Tuesday? In terms of crowds, is weekday better? We are going in early April.