It's for your son to decide not you, but given the facts, everything seems fair except the felony charge. try to convince your son he needs to insist on a misdemeanor charge even if he has to serve a few more days in jail. It's worth the effort. Residential burglary is a serious crime no matter how lightly he is getting off--this time.
This is your son's decision. Generally public defenders do good work for 1st offenders and understand the limitations of offers, compared to the ultimate consequence and risk of the higher charge. If your son's end result is a misdeanor conviction, even with a little jail time, then your son has done pretty good--since he did walk into someone's home and take the property of another. If your son is as good a guy as you want to believe, then he should be able to stay out of trouble long enough to eventually have that conviction expunged from his record at a later time.
There are some facts requiring clarification before an assessment of fairness can be offered.
First: Was the garage attached to the house or separate from it? If separate a charge of residential burglary may not lie. Theft and criminal trespass still would but these are much less serious offenses.
Second: Where did the police recover the bicycle? If from the back yard then I assume as is parent you had access to it and permission to consent to its search. What about the shed? Did your son have exclusive access to it? If so, your consent may not have been valid. These issues may improve your son's bargaining position or may require an outright dismissal as the police may have violated his fourth amendment rights.
As has been stated, it is you son's decision. My experience is that the local Public Defender knows what is reasonable in the community from the daily practice.
It is important that your son understands the implications of the conviction for employment and for use as a prior. (I am in California and we have the Three Strikes laws.)
Plea bargaining is just like any other sort of negotiation. The more the defense has to trade the better outcome he can negotiate. The best plea offers are made to defendants who have some legal or factual defense to mount if the case is litigated. For example, sometimes a better plea offer is made to a defendant who agrees not to litigate a sound legal motion. Without seeing the police reports in your son's case, it is difficult to know what, if any, defenses or legal motions might have been available to him.
Usually public defenders are in a very good position to know what plea offers are typical or even possible in a jurisdiction.
As others have said, your son would be in a much better position if he could plead to a misdemeanor and avoid a felony conviction. That said, sometimes an Oregon felony conviction can be reduced to a misdemeanor at the end of a successful probation. Ask your son's attorney whether the relief in ORS 161.705 might be available under the terms of the current plea offer.