Io evito l’orario di punta e vado in bicicletta in città.

In Italian, verbs are conjugated to show the subject, so you can drop Io and still know who’s acting. Saying
• Evito l’orario di punta e vado in bicicletta in città
is perfectly normal. Including Io adds emphasis or clarity, especially if you want to contrast with someone else.

The verb evitare is transitive, so it directly governs its object. You say evito l’orario (I avoid the time). If you want to avoid doing something, you switch to evitare di + infinitive, for example:
• Evito di viaggiare di notte (I avoid traveling at night).

• Di = of
• Punta = point, tip, peak
So di punta conveys “at the peak,” describing the highest-intensity time. It’s an idiomatic way to mark something as happening at its busiest or most critical moment.

When talking about means of transportation or how you move, Italian uses:
• in for vehicles with wheels: in macchina, in treno, in bicicletta
• a for animals or when literally “on” something: a cavallo (on horseback), a piedi (on foot).

To indicate location inside a place, Italian normally uses in + noun for cities, regions, countries:
• in città, in Italia, in montagna.
Articles can drop after in when the noun is generic, as with città here.

E is the coordinating conjunction meaning and, used to link two independent clauses:
• evito l’orario di punta
e
• vado in bicicletta in città.