Hello I'm going to Rome on a honeymoon. I'm staying in Piazza di Spagna, I hope this is a good choice.
I'm interested in food and I was thinking to take a food tour. Does anyone know Do Eat Better Food Tours? I've read very good reviews. I don't want to do touristy thing and I've read their food tours are far way for being touristy and their group are very small.
Last question, can you suggest a special restaurant to celebrate our first day in Rome?

Where will you be staying in Rome? What are you budgeting for this meal, including wine (if you drink wine). If you are arriving jet lagged, you might feel more in the mood to celebrate if you stay in the neighborhood of your hotel, so you can walk home easily. Many people arriving on a trans-continental flight have a hard time staying awake once the sun goes down, and dinner in Rome really doesn't start until 8pm, and there tends to be a long time between courses. You might prefer to go out for a wonderful cocktail at sunset, and put off having a great dinner to when you are no longer jet lagged.

You made a typo in your original post that makes it hard to understand what you've read about Better Food Tours (I don't know anything about them, but you might want to re-state your post).

We did the Testaccio tour with Eating Italy and were very pleased because it took us to a neighborhood we had not previously visited. There were 7 food stops, including lunch, and a tour of the Protestant Cemetery where Keats and Shelley are buried. This company also has day and evening tours in the Trastevere neighborhood.

We loved the Eating Italy food tour of Testaccio too. I highly recommend it.

We did a food tour with Elizabeth Minchilli that was excellent. She also has a wonderful app called Eat Rome to help you with restaurant choices.

Not sure of your price range for a special first night. In fact, we did the food tour tour with Elizabeth as a way to learn our way around and snack from site to site and not sit down for a full dinner. Sometimes a big dinner that first night, is a let down...I am less hungry when I am tired and jet lagged.

I also just did the Testaccio tour with Eating Italy and enjoyed it very much. However, I did this because I have been in Rome many times and was looking for something different to do. If this is your first time in Rome not sure if I would advice spending 4-5 hrs on this , unless your heart is set on doing a "food tour".