Riga is quite safe, but you should use common sense about your wallet. In Old Town be aware of pick pockets. I have not seen any but I know they exist.
It gets dark around 10PM in June, I suppose in July it will get dark even later. Radisson hotel might not be a good location. It is too far to walk to Old Town, too short to take a taxi. I suggest Metropole hotel. Good location, good brakefast. I paid 55 EUR back in March, 2005. Or Centra hotel is also good. Beware of taxi. The Red taxi is better. The white ones will rip you off. Avoid any taxi in Old Town.