No. The Sims 2 on PlayStation 2 does not have a Downtown area (or any sub-neighborhoods like University, Shopping, or Vacation).
| Feature | PC (Base + Nightlife) | PS2 |
|---|---|---|
| Downtown / Sub-hoods | Yes (Nightlife EP) | No |
| Open Neighborhood | Yes | No (Loading screens between lots) |
| Direct Control | No (Mods only) | Yes |
| Story Mode | No | Yes |
| 2-Player Local | No | Yes |
If you want Downtown, you need the PC version + Nightlife Expansion Pack (or The Sims 2 Ultimate Collection on Origin/EA App).